Question

factorise (25x^2+9y^2+64-15xy+24y+40x) (-5x-3y+8)​

Answer 1

Answer:

$\mathrm{Expand\:\left(25x^2+9y^2+64-15xy+24y+40x\right)\left(-5x-3y+8\right):\quad -27y^3-125x^3-360xy+512}$

Step-by-step explanation:

$\mathrm{\left(25x^2+9y^2+64-15xy+24y+40x\right)\left(-5x-3y+8\right)}$

$\mathrm{Apply\:the\:distributive\:law:\quad \left(a+b\right)\left(x+y+z\right)=ax+ay+az+bx+by+bz}$

$[\left(25x^2+9y^2+64-15xy+24y+40x\right)\left(-5x-3y+8\right)=25x^2\left(-5x\right)$

$+25x^2\left(-3y\right)+25x^2\cdot \:8+9 y^2 (-5x)+9y^2 (-3y) +9y^2\times 8+64 (-5x)$

$+64(-3y)+64\times8-15xy(-5x)-15xy (-3y) -15xy \times 8+24y(-5x)+24y(-3y)+24y\times8+40x(-5x)+40x(-3y)+40x\times8]$

$=25x^2\left(-5x\right)+25x^2\left(-3y\right)+25x^2\cdot \:8+9y^2\left(-5x\right)+9y^2\left(-3y\right)+9y^2\cdot \:8+64\left(-5x\right)+64\left(-3y\right)+64\times8 -15xy(-5x)-15xy(-3y)-15xy\times8+24y(-5x)+24y(-3y)24y\times8+40x(-5x)+40x(-3y)+40x\times8$

$\mathrm{=-27y^3-125x^3-360xy+512}$