Question

10. Multiplica los siguientes polinomios a) (5x2 – 3x) (2x - 8) b) (4m²n + 7mn?)(-3m²n + 2mn2) c) (8a3b - 5ab2)(-3a²b + 9ab2 - 4) d) (2x2y - 7xy)(5x)(3x2y - 6xy) -​

Answer 1

Respuesta:

a)$10x^3-46x^2+24x$

b)$-12m^4n^2+8m^3n^3-21m^3n^2+14m^2n^3$

c)$-24a^5b^2+72a^4b^3-32a^3b+15a^3b^3-45a^2b^4+20ab^2$

d)$30x^5y^2-165x^4y^2+210x^3y^2$

Explicación paso a paso:

a)$\left(5x^2-3x\right)\left(2x-8\right)$

Simplificar:

= $x^2\cdot \:2x+5x^2\left(-8\right)-3x\cdot \:2x-3x\left(-8\right)$

=$10x^3-46x^2+24x$

b)$(4m^{2} n + 7mn)(-3m^{2} n + 2mn^{2} )$

Simplificar:

=$4m^2n\left(-3m^2n\right)+4m^2n\cdot \:2mn^2+7mn\left(-3m^2n\right)+7mn\cdot \:2mn^2$

=$-12m^4n^2+8m^3n^3-21m^3n^2+14m^2n^3$

c)$(8a3b - 5ab^2)(-3a^2b + 9ab^2 - 4)$

Simplificar:

=$8a^3b\left(-3a^2b\right)+8a^3b\cdot \:9ab^2+8a^3b\left(-4\right)-5ab^2\left(-3a^2b\right)-5ab^2\cdot \:9ab^2-5ab^2\left(-4\right)$

=$-24a^5b^2+72a^4b^3-32a^3b+15a^3b^3-45a^2b^4+20ab^2$

d)$\left(2x2y\:-\:7xy\right)\left(5x\right)\left(3x2y\:-\:6xy\right)\:$

Simplificar:

=$5x\left(6x^4y^2-33x^3y^2+42x^2y^2\right)=5x\cdot \:6x^4y^2+5x\left(-33x^3y^2\right)+5x\cdot \:42x^2y^2$

=$30x^5y^2-165x^4y^2+210x^3y^2$