Ejercicios con expresiones algebraicas
- \((8x^9y^4z^3) \cdot(2x^3y^6z^4)\) Resp: \(16x^{12}y^{10}z^{7}\).
- \((8x^2y^2z^9) \cdot(2x^9y^6z^4)\) Resp: \(16x^{11}y^{8}z^{13}\).
- \((6x^9y^2z^8) \cdot(3x^5y^3z^2)\) Resp: \(18x^{14}y^{5}z^{10}\).
- \((2x^5y^3z^3) \cdot(5x^3y^3z^8)\) Resp: \(10x^{8}y^{6}z^{11}\).
- \((-9x^5y^3z^6) \cdot(3x^4y^8z^8)\) Resp: \(-27x^{9}y^{11}z^{14}\).
- \((2x^5y^6z^2) \cdot(2x^4y^3z^7)\) Resp: \(4x^{9}y^{9}z^{9}\).
- \((6x^2y^5z^4) \cdot(4x^4y^5z^8)\) Resp: \(24x^{6}y^{10}z^{12}\).
- \((5x^4y^9z^4) \cdot(7x^2y^9z^2)\) Resp: \(35x^{6}y^{18}z^{6}\).
- \((2x^9y^7z^6) \cdot(4x^9y^3z^3)\) Resp: \(8x^{18}y^{10}z^{9}\).
- \((7x^9y^5z^2) \cdot(-9x^2y^8z^2)\) Resp: \(-63x^{11}y^{13}z^{4}\).
- \((-3x^9y^8z^5) \cdot(4x^2y^8z^9)\) Resp: \(-12x^{11}y^{16}z^{14}\).
- \((3x^4y^2z^8) \cdot(-6x^7y^7z^8)\) Resp: \(-18x^{11}y^{9}z^{16}\).
- \((-6x^5y^2z^5) \cdot(-7x^6y^7z^2)\) Resp: \(42x^{11}y^{9}z^{7}\).
- \((3x^8y^3z^2) \cdot(-3x^5y^4z^6)\) Resp: \(-9x^{13}y^{7}z^{8}\).
- \((5x^7y^2z^7) \cdot(-6x^9y^7z^3)\) Resp: \(-30x^{16}y^{9}z^{10}\).
- \((3x^3y^5z^6) \cdot(9x^5y^4z^4)\) Resp: \(27x^{8}y^{9}z^{10}\).
- \((4x^7y^2z^2) \cdot(-5x^4y^3z^7)\) Resp: \(-20x^{11}y^{5}z^{9}\).
- \((-9x^5y^6z^6) \cdot(5x^7y^8z^3)\) Resp: \(-45x^{12}y^{14}z^{9}\).
- \((8x^6y^7z^9) \cdot(-6x^3y^7z^7)\) Resp: \(-48x^{9}y^{14}z^{16}\).
- \((-4x^3y^7z^5) \cdot(8x^7y^3z^2)\) Resp: \(-32x^{10}y^{10}z^{7}\).
- \((-2x^3y^9z^4) \cdot(-4x^6y^9z^7)\) Resp: \(8x^{9}y^{18}z^{11}\).
- \((7x^6y^9z^5) \cdot(2x^6y^5z^3)\) Resp: \(14x^{12}y^{14}z^{8}\).
- \((6x^2y^5z^8) \cdot(-6x^4y^9z^8)\) Resp: \(-36x^{6}y^{14}z^{16}\).
- \((6x^9y^4z^6) \cdot(4x^3y^7z^4)\) Resp: \(24x^{12}y^{11}z^{10}\).
- \((-5x^8y^7z^9) \cdot(-7x^9y^9z^9)\) Resp: \(35x^{17}y^{16}z^{18}\).
- \((-2x^6y^5z^2) \cdot(9x^9y^4z^9)\) Resp: \(-18x^{15}y^{9}z^{11}\).
- \((8x^4y^8z^3) \cdot(-5x^7y^5z^9)\) Resp: \(-40x^{11}y^{13}z^{12}\).
- \((4x^2y^3z^3) \cdot(-8x^9y^2z^4)\) Resp: \(-32x^{11}y^{5}z^{7}\).
- \((-8x^2y^3z^6) \cdot(2x^6y^6z^6)\) Resp: \(-16x^{8}y^{9}z^{12}\).
- \((-4x^9y^9z^2) \cdot(-9x^5y^5z^3)\) Resp: \(36x^{14}y^{14}z^{5}\).
- \((2x^6y^4z^9) \cdot(3x^6y^7z^2)\) Resp: \(6x^{12}y^{11}z^{11}\).
- \((4x^8y^7z^6) \cdot(-7x^6y^8z^3)\) Resp: \(-28x^{14}y^{15}z^{9}\).
- \((-3x^2y^3z^9) \cdot(-7x^6y^4z^9)\) Resp: \(21x^{8}y^{7}z^{18}\).
- \((2x^7y^3z^4) \cdot(-4x^6y^2z^8)\) Resp: \(-8x^{13}y^{5}z^{12}\).
- \((-9x^9y^7z^6) \cdot(-8x^8y^5z^5)\) Resp: \(72x^{17}y^{12}z^{11}\).
- \((6x^3y^6z^3) \cdot(-8x^5y^2z^6)\) Resp: \(-48x^{8}y^{8}z^{9}\).
- \((-9x^2y^2z^5) \cdot(-4x^3y^8z^2)\) Resp: \(36x^{5}y^{10}z^{7}\).
- \((9x^7y^2z^7) \cdot(5x^4y^4z^8)\) Resp: \(45x^{11}y^{6}z^{15}\).
- \((8x^4y^6z^6) \cdot(7x^2y^6z^6)\) Resp: \(56x^{6}y^{12}z^{12}\).
- \((-4x^9y^9z^5) \cdot(4x^3y^4z^4)\) Resp: \(-16x^{12}y^{13}z^{9}\).
- \((8x^3y^3z^6) \cdot(-8x^6y^4z^6)\) Resp: \(-64x^{9}y^{7}z^{12}\).
- \((-6x^9y^9z^2) \cdot(2x^2y^3z^7)\) Resp: \(-12x^{11}y^{12}z^{9}\).
- \((6x^7y^3z^5) \cdot(7x^3y^5z^4)\) Resp: \(42x^{10}y^{8}z^{9}\).
- \((-3x^7y^3z^3) \cdot(7x^8y^3z^3)\) Resp: \(-21x^{15}y^{6}z^{6}\).
- \((9x^4y^4z^8) \cdot(9x^3y^2z^9)\) Resp: \(81x^{7}y^{6}z^{17}\).
- \((5x^6y^2z^7) \cdot(-3x^7y^9z^4)\) Resp: \(-15x^{13}y^{11}z^{11}\).
- \((4x^4y^9z^2) \cdot(-9x^2y^8z^7)\) Resp: \(-36x^{6}y^{17}z^{9}\).
- \((-4x^3y^7z^6) \cdot(7x^9y^6z^6)\) Resp: \(-28x^{12}y^{13}z^{12}\).
- \((-2x^8y^7z^4) \cdot(9x^4y^8z^9)\) Resp: \(-18x^{12}y^{15}z^{13}\).
- \((9x^5y^3z^5) \cdot(5x^2y^6z^4)\) Resp: \(45x^{7}y^{9}z^{9}\).
- \(x^9y^7z^9\cdot \left( 9x^2y^2z^8+8x^6y^7z^2\right) +x^3y^8z^5 \cdot \left( 7x^{8}y^{1}z^{12}+2x^{12}y^{6}z^{6}\right)\) Resp: \(16x^{11}y^{9}z^{17}+10x^{15}y^{14}x^{11}\).
- \(x^6y^2z^4\cdot \left( 3x^3y^3z^4+5x^7y^8z^4\right) +x^4y^3z^3 \cdot \left( 5x^{5}y^{2}z^{5}+7x^{9}y^{7}z^{5}\right)\) Resp: \(8x^{9}y^{5}z^{8}+12x^{13}y^{10}x^{8}\).
- \(x^5y^2z^6\cdot \left( 3x^4y^8z^6+3x^4y^4z^6\right) +x^6y^5z^4 \cdot \left( 8x^{3}y^{5}z^{8}+9x^{3}y^{1}z^{8}\right)\) Resp: \(11x^{9}y^{10}z^{12}+12x^{9}y^{6}x^{12}\).
- \(x^6y^2z^4\cdot \left( 3x^3y^9z^5+3x^3y^3z^5\right) +x^9y^9z^3 \cdot \left( 6x^{0}y^{2}z^{6}+5x^{0}y^{-4}z^{6}\right)\) Resp: \(9x^{9}y^{11}z^{9}+8x^{9}y^{5}x^{9}\).
- \(x^9y^2z^9\cdot \left( 6x^6y^3z^2+6x^5y^3z^6\right) +x^7y^4z^5 \cdot \left( 4x^{8}y^{1}z^{6}+9x^{7}y^{1}z^{10}\right)\) Resp: \(10x^{15}y^{5}z^{11}+15x^{14}y^{5}x^{15}\).
- \(x^5y^5z^5\cdot \left( 2x^2y^4z^8+8x^8y^7z^9\right) +x^2y^4z^5 \cdot \left( 7x^{5}y^{5}z^{8}+8x^{11}y^{8}z^{9}\right)\) Resp: \(9x^{7}y^{9}z^{13}+16x^{13}y^{12}x^{14}\).
- \(x^5y^3z^5\cdot \left( 2x^2y^8z^5+6x^2y^5z^4\right) +x^4y^4z^4 \cdot \left( 2x^{3}y^{7}z^{6}+7x^{3}y^{4}z^{5}\right)\) Resp: \(4x^{7}y^{11}z^{10}+13x^{7}y^{8}x^{9}\).
- \(x^7y^9z^5\cdot \left( 8x^7y^4z^2+9x^3y^8z^9\right) +x^3y^5z^9 \cdot \left( 2x^{11}y^{8}z^{-2}+7x^{7}y^{12}z^{5}\right)\) Resp: \(10x^{14}y^{13}z^{7}+16x^{10}y^{17}x^{14}\).
- \(x^8y^7z^7\cdot \left( 4x^2y^5z^9+6x^7y^2z^4\right) +x^5y^6z^5 \cdot \left( 8x^{5}y^{6}z^{11}+6x^{10}y^{3}z^{6}\right)\) Resp: \(12x^{10}y^{12}z^{16}+12x^{15}y^{9}x^{11}\).
- \(x^5y^6z^9\cdot \left( 9x^5y^4z^2+4x^5y^3z^8\right) +x^4y^8z^8 \cdot \left( 9x^{6}y^{2}z^{3}+5x^{6}y^{1}z^{9}\right)\) Resp: \(18x^{10}y^{10}z^{11}+9x^{10}y^{9}x^{17}\).
- \(x^2y^6z^5\cdot \left( 3x^7y^6z^5+4x^6y^3z^8\right) +x^3y^8z^2 \cdot \left( 9x^{6}y^{4}z^{8}+5x^{5}y^{1}z^{11}\right)\) Resp: \(12x^{9}y^{12}z^{10}+9x^{8}y^{9}x^{13}\).
- \(x^3y^8z^3\cdot \left( 3x^8y^4z^7+4x^2y^5z^9\right) +x^8y^9z^5 \cdot \left( 2x^{3}y^{3}z^{5}+8x^{-3}y^{4}z^{7}\right)\) Resp: \(5x^{11}y^{12}z^{10}+12x^{5}y^{13}x^{12}\).
- \(x^2y^5z^5\cdot \left( 6x^3y^4z^8+7x^3y^2z^6\right) +x^2y^6z^6 \cdot \left( 8x^{3}y^{3}z^{7}+9x^{3}y^{1}z^{5}\right)\) Resp: \(14x^{5}y^{9}z^{13}+16x^{5}y^{7}x^{11}\).
- \(x^5y^7z^7\cdot \left( 9x^7y^9z^9+7x^2y^6z^3\right) +x^4y^9z^3 \cdot \left( 7x^{8}y^{7}z^{13}+2x^{3}y^{4}z^{7}\right)\) Resp: \(16x^{12}y^{16}z^{16}+9x^{7}y^{13}x^{10}\).
- \(x^9y^6z^2\cdot \left( 2x^4y^6z^3+9x^5y^3z^2\right) +x^8y^4z^6 \cdot \left( 8x^{5}y^{8}z^{-1}+4x^{6}y^{5}z^{-2}\right)\) Resp: \(10x^{13}y^{12}z^{5}+13x^{14}y^{9}x^{4}\).
- \(x^4y^4z^3\cdot \left( 5x^2y^8z^2+7x^4y^5z^3\right) +x^3y^5z^3 \cdot \left( 8x^{3}y^{7}z^{2}+3x^{5}y^{4}z^{3}\right)\) Resp: \(13x^{6}y^{12}z^{5}+10x^{8}y^{9}x^{6}\).
- \(x^9y^9z^2\cdot \left( 2x^5y^8z^3+2x^8y^7z^8\right) +x^6y^8z^6 \cdot \left( 5x^{8}y^{9}z^{-1}+5x^{11}y^{8}z^{4}\right)\) Resp: \(7x^{14}y^{17}z^{5}+7x^{17}y^{16}x^{10}\).
- \(x^4y^4z^5\cdot \left( 8x^6y^6z^6+4x^4y^6z^2\right) +x^4y^2z^8 \cdot \left( 2x^{6}y^{8}z^{3}+8x^{4}y^{8}z^{-1}\right)\) Resp: \(10x^{10}y^{10}z^{11}+12x^{8}y^{10}x^{7}\).
- \(x^6y^7z^5\cdot \left( 9x^9y^6z^6+9x^4y^9z^6\right) +x^9y^4z^4 \cdot \left( 2x^{6}y^{9}z^{7}+3x^{1}y^{12}z^{7}\right)\) Resp: \(11x^{15}y^{13}z^{11}+12x^{10}y^{16}x^{11}\).
- \(x^4y^2z^9\cdot \left( 9x^9y^7z^4+2x^2y^6z^7\right) +x^2y^3z^7 \cdot \left( 2x^{11}y^{6}z^{6}+9x^{4}y^{5}z^{9}\right)\) Resp: \(11x^{13}y^{9}z^{13}+11x^{6}y^{8}x^{16}\).
- \(x^3y^7z^6\cdot \left( 6x^6y^6z^6+6x^9y^3z^3\right) +x^9y^6z^5 \cdot \left( 2x^{0}y^{7}z^{7}+3x^{3}y^{4}z^{4}\right)\) Resp: \(8x^{9}y^{13}z^{12}+9x^{12}y^{10}x^{9}\).
- \(x^7y^9z^2\cdot \left( 8x^6y^2z^3+9x^4y^6z^9\right) +x^5y^5z^3 \cdot \left( 4x^{8}y^{6}z^{2}+3x^{6}y^{10}z^{8}\right)\) Resp: \(12x^{13}y^{11}z^{5}+12x^{11}y^{15}x^{11}\).
- \(x^5y^4z^6\cdot \left( 9x^7y^5z^7+6x^4y^3z^3\right) +x^3y^4z^4 \cdot \left( 2x^{9}y^{5}z^{9}+8x^{6}y^{3}z^{5}\right)\) Resp: \(11x^{12}y^{9}z^{13}+14x^{9}y^{7}x^{9}\).
- \(x^4y^2z^2\cdot \left( 5x^7y^3z^8+4x^7y^5z^7\right) +x^2y^3z^8 \cdot \left( 8x^{9}y^{2}z^{2}+6x^{9}y^{4}z^{1}\right)\) Resp: \(13x^{11}y^{5}z^{10}+10x^{11}y^{7}x^{9}\).
- \(x^7y^7z^2\cdot \left( 3x^9y^2z^3+5x^5y^5z^3\right) +x^2y^8z^8 \cdot \left( 6x^{14}y^{1}z^{-3}+5x^{10}y^{4}z^{-3}\right)\) Resp: \(9x^{16}y^{9}z^{5}+10x^{12}y^{12}x^{5}\).
- \(x^9y^9z^4\cdot \left( 9x^6y^8z^6+2x^3y^5z^4\right) +x^6y^3z^9 \cdot \left( 5x^{9}y^{14}z^{1}+6x^{6}y^{11}z^{-1}\right)\) Resp: \(14x^{15}y^{17}z^{10}+8x^{12}y^{14}x^{8}\).
- \(x^3y^4z^7\cdot \left( 2x^5y^3z^4+7x^3y^3z^5\right) +x^2y^3z^4 \cdot \left( 5x^{6}y^{4}z^{7}+4x^{4}y^{4}z^{8}\right)\) Resp: \(7x^{8}y^{7}z^{11}+11x^{6}y^{7}x^{12}\).
- \(x^9y^5z^6\cdot \left( 5x^2y^7z^4+3x^7y^6z^8\right) +x^4y^5z^6 \cdot \left( 8x^{7}y^{7}z^{4}+4x^{12}y^{6}z^{8}\right)\) Resp: \(13x^{11}y^{12}xz^{10}+7x^{16}y^{11}x^{14}\).
- \(x^7y^6z^2\cdot \left( 7x^5y^4z^3+3x^4y^2z^2\right) +x^6y^5z^4 \cdot \left( 2x^{6}y^{5}z^{1}+6x^{5}y^{3}z^{0}\right)\) Resp: \(9x^{12}y^{10}z^{5}+9x^{11}y^{8}x^{4}\).
- \(x^4y^3z^6\cdot \left( 6x^6y^3z^7+8x^7y^8z^6\right) +x^7y^2z^2 \cdot \left( 5x^{3}y^{4}z^{11}+6x^{4}y^{9}z^{10}\right)\) Resp: \(11x^{10}y^{6}z^{13}+14x^{11}y^{11}x^{12}\).
- \(x^6y^3z^3\cdot \left( 3x^5y^9z^6+8x^5y^6z^5\right) +x^4y^3z^7 \cdot \left( 8x^{7}y^{9}z^{2}+5x^{7}y^{6}z^{1}\right)\) Resp: \(11x^{11}y^{12}z^{9}+13x^{11}y^{9}x^{8}\).
- \(x^8y^6z^3\cdot \left( 2x^5y^2z^6+4x^5y^4z^5\right) +x^5y^2z^7 \cdot \left( 3x^{8}y^{6}z^{2}+8x^{8}y^{8}z^{1}\right)\) Resp: \(5x^{13}y^{8}z^{9}+12x^{13}y^{10}x^{8}\).
- \(x^3y^8z^5\cdot \left( 5x^2y^6z^4+3x^6y^2z^4\right) +x^6y^9z^6 \cdot \left( 8x^{-1}y^{5}z^{3}+9x^{3}y^{1}z^{3}\right)\) Resp: \(13x^{5}y^{14}z^{9}+12x^{9}y^{10}x^{9}\).
- \(x^2y^9z^9\cdot \left( 8x^7y^6z^6+5x^2y^5z^6\right) +x^2y^6z^2 \cdot \left( 6x^{7}y^{9}z^{13}+2x^{2}y^{8}z^{13}\right)\) Resp: \(14x^{9}y^{15}z^{15}+7x^{4}y^{14}x^{15}\).
- \(x^5y^7z^5\cdot \left( 7x^7y^9z^4+2x^2y^5z^2\right) +x^5y^8z^5 \cdot \left( 9x^{7}y^{8}z^{4}+6x^{2}y^{4}z^{2}\right)\) Resp: \(16x^{12}y^{16}z^{9}+8x^{7}y^{12}x^{7}\).
- \(x^3y^6z^2\cdot \left( 5x^8y^4z^8+4x^4y^4z^9\right) +x^3y^8z^7 \cdot \left( 4x^{8}y^{2}z^{3}+6x^{4}y^{2}z^{4}\right)\) Resp: \(9x^{11}y^{10}z^{10}+10x^{7}y^{10}x^{11}\).
- \(x^3y^9z^4\cdot \left( 4x^9y^2z^2+8x^5y^8z^3\right) +x^2y^3z^6 \cdot \left( 6x^{10}y^{8}z^{0}+5x^{6}y^{14}z^{1}\right)\) Resp: \(10x^{12}y^{11}z^{6}+13x^{8}y^{17}x^{7}\).
- \(x^5y^6z^6\cdot \left( 5x^8y^5z^5+2x^6y^7z^5\right) +x^4y^9z^7 \cdot \left( 8x^{9}y^{2}z^{4}+3x^{7}y^{4}z^{4}\right)\) Resp: \(13x^{13}y^{11}z^{11}+5x^{11}y^{13}x^{11}\).
- \(x^3y^6z^9\cdot \left( 4x^2y^7z^4+4x^3y^6z^8\right) +x^7y^8z^3 \cdot \left( 8x^{-2}y^{5}z^{10}+4x^{-1}y^{4}z^{14}\right)\) Resp: \(12x^{5}y^{13}z^{13}+8x^{6}y^{12}x^{17}\).
- \(x^2y^6z^8\cdot \left( 9x^3y^2z^8+9x^7y^8z^7\right) +x^6y^9z^7 \cdot \left( 3x^{-1}y^{-1}z^{9}+7x^{3}y^{5}z^{8}\right)\) Resp: \(12x^{5}y^{8}z^{16}+16x^{9}y^{14}x^{15}\).
- \(x^2y^8z^8\cdot \left( 7x^9y^7z^2+5x^4y^6z^8\right) +x^9y^3z^9 \cdot \left( 7x^{2}y^{12}z^{1}+8x^{-3}y^{11}z^{7}\right)\) Resp: \(14x^{11}y^{15}z^{10}+13x^{6}y^{14}x^{16}\).
- \(x^8y^5z^2\cdot \left( 9x^5y^8z^2+8x^8y^6z^9\right) +x^9y^2z^2 \cdot \left( 9x^{4}y^{11}z^{2}+8x^{7}y^{9}z^{9}\right)\) Resp: \(18x^{13}y^{13}z^{4}+16x^{16}y^{11}x^{11}\).
- \(x^4y^5z^5\cdot \left( 2x^5y^8z^5+8x^2y^3z^8\right) +x^5y^3z^9 \cdot \left( 7x^{4}y^{10}z^{1}+2x^{1}y^{5}z^{4}\right)\) Resp: \(9x^{9}y^{13}z^{10}+10x^{6}y^{8}x^{13}\).
- \(x^8y^4z^7\cdot \left( 2x^4y^6z^3+9x^9y^7z^7\right) +x^3y^8z^6 \cdot \left( 7x^{9}y^{2}z^{4}+8x^{14}y^{3}z^{8}\right)\) Resp: \(9x^{12}y^{10}z^{10}+17x^{17}y^{11}x^{14}\).
- \(x^7y^8z^2\cdot \left( 4x^2y^2z^2+6x^4y^8z^6\right) +x^8y^8z^5 \cdot \left( 2x^{1}y^{2}z^{-1}+9x^{3}y^{8}z^{3}\right)\) Resp: \(6x^{9}y^{10}z^{4}+15x^{11}y^{16}x^{8}\).
- \(x^9y^4z^2\cdot \left( 7x^5y^6z^7+8x^6y^6z^7\right) +x^3y^3z^6 \cdot \left( 9x^{11}y^{7}z^{3}+6x^{12}y^{7}z^{3}\right)\) Resp: \(16x^{14}y^{10}z^{9}+14x^{15}y^{10}x^{9}\).
- \(x^3y^8z^3\cdot \left( 7x^2y^2z^7+9x^4y^9z^9\right) +x^6y^9z^7 \cdot \left( 4x^{-1}y^{1}z^{3}+8x^{1}y^{8}z^{5}\right)\) Resp: \(11x^{5}y^{10}z^{10}+17x^{7}y^{17}x^{12}\).
- \(x^5y^2z^8\cdot \left( 3x^9y^6z^5+8x^7y^7z^6\right) +x^3y^2z^9 \cdot \left( 2x^{11}y^{6}z^{4}+7x^{9}y^{7}z^{5}\right)\) Resp: \(5x^{14}y^{8}z^{13}+15x^{12}y^{9}x^{14}\).
- \(x^3y^5z^6\cdot \left( 4x^5y^8z^9+5x^5y^9z^3\right) +x^7y^7z^4 \cdot \left( 4x^{1}y^{6}z^{11}+8x^{1}y^{7}z^{5}\right)\) Resp: \(8x^{8}y^{13}z^{15}+13x^{8}y^{14}x^{9}\).
- \(x^4y^5z^2\cdot \left( 6x^6y^3z^5+5x^7y^7z^8\right) +x^8y^5z^8 \cdot \left( 8x^{2}y^{3}z^{-1}+2x^{3}y^{7}z^{2}\right)\) Resp: \(14x^{10}y^{8}z^{7}+7x^{11}y^{12}x^{10}\).
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