Question

Ocupo ayudaaa, hoy por mi mañana por ustedes):

Answer 1

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

$a=2x^2,\:b=-5y^3,\:c=3x^2,\:d=y^3$

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

$=2\cdot \:3x^2x^2+2x^2y^3-5\cdot \:3x^2y^3-5y^3y^3$

$2\cdot \:3x^2x^2=6x^4$

$5\cdot \:3x^2y^3=15x^2y^3$

$5y^3y^3=5y^6$

$=6x^4+2x^2y^3-15x^2y^3-5y^6$

$=6x^4-13x^2y^3-5y^6$

b) $\left(xm-3yn\right)\left(3x^2+2y^2\right)$

$a=xm,\:b=-3yn,\:c=3x^2,\:d=2y^2$

$=xm\cdot \:3x^2+xm\cdot \:2y^2+\left(-3yn\right)\cdot \:3x^2+\left(-3yn\right)\cdot \:2y^2$

$=3mx^2x+2mxy^2-3\cdot \:3nx^2y-3\cdot \:2ny^2y$

$3mx^2x=3mx^3$

$3\cdot \:3nx^2y=9nx^2y$

$3\cdot \:2ny^2y=6ny^3$

$=3mx^3+2mxy^2-9nx^2y-6ny^3$

c) $\frac{2x^3+x^2-8x+2}{2x-3}$

$=x^2+\frac{4x^2-8x+2}{2x-3}$

$=x^2+2x+\frac{-2x+2}{2x-3}$

$=x^2+2x-1+\frac{-1}{2x-3}$

d) $\frac{2x^2+5xy-3y^2}{x+3y}$

$2x^2+5xy-3y^2$

$=\left(2x^2-xy\right)+\left(6xy-3y^2\right)$

$=x\left(2x-y\right)+3y\left(2x-y\right)$

$=\left(2x-y\right)\left(x+3y\right)$

$=\frac{\left(2x-y\right)\left(x+3y\right)}{x+3y}$

$=2x-y$

¡Espero haberte ayudado Gaelmillanpen6mm!