# What is the standard form of  y= (2x+8)^3-(5x-3)^2?

May 2, 2016

$y = 8 {x}^{3} + 71 {x}^{2} + 414 x + 503$

#### Explanation:

Multiply out and simplify, using the binomial expansions:

${\left(a + b\right)}^{3} = {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

as follows:

$y = {\left(2 x + 8\right)}^{3} - {\left(5 x - 3\right)}^{2}$

$= \left({\left(2 x\right)}^{3} + 3 {\left(2 x\right)}^{2} \left(8\right) + 3 \left(2 x\right) {8}^{2} + {8}^{3}\right) - \left({\left(5 x\right)}^{2} - 2 \left(5 x\right) \left(3\right) + {3}^{2}\right)$

$= \left(8 {x}^{3} + 96 {x}^{2} + 384 x + 512\right) - \left(25 {x}^{2} - 30 x + 9\right)$

$= 8 {x}^{3} + \left(96 - 25\right) {x}^{2} + \left(384 + 30\right) x + \left(512 - 9\right)$

$= 8 {x}^{3} + 71 {x}^{2} + 414 x + 503$

Standard form consists of a sum of terms in decreasing order of degree, as we have arrived at.