What is the standard form of $y = {(- 4 x + 4)}^{3} - {(5 x + 12)}^{2}$ $y= (-4x+4)^3-(5x+12)^2$ ?

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Answer 1 · 2018-03-11T05:30:42

$y = - 64 x^{3} + 167 x^{2} - 312 x - 80$ $y=-64x^3+167x^2-312x-80$

The standard form of a cubic function is :

$y = a x^{3} + b x^{2} + c x + d$ $y=ax^3+bx^2+cx+d$

Therefore after expanding

${(- 4 x - 4)}^{3}$ $(-4x-4)^3$

= $- 64 x^{3} + 192 x^{2} - 192 x + 64$ $-64x^3+192x^2-192x+64$

and

${(5 x + 12)}^{2}$ $(5x+12)^2$

= $25 x^{2} + 120 x + 144$ $25x^2+120x+144$

We can join the 2 expressions

$y = (- 64 x^{3} + 192 x^{2} - 192 x + 64) - (25 x^{2} + 120 x + 144)$ $y=(-64x^3+192x^2-192x+64) - (25x^2+120x+144)$

$y = - 64 x^{3} + 167 x^{2} - 312 x - 80$ $y=-64x^3+167x^2-312x-80$

What is the standard form of y=(−4x+4)3−(5x+12)2 y= (-4x+4)^3-(5x+12)^2?