# What is the standard form of  y= (5x+3)^3+(7x-13)^2?

Jan 18, 2017

${\left(5 x + 3\right)}^{3} + {\left(7 x - 13\right)}^{2} = 125 {x}^{3} + 274 {x}^{2} - 47 x + 196$

#### Explanation:

In general we have:

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

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

So:

${\left(7 x - 13\right)}^{2} = {\left(7 x\right)}^{2} - 2 \left(7 x\right) \left(13\right) + {13}^{2}$

$\textcolor{w h i t e}{{\left(7 x - 13\right)}^{2}} = 49 {x}^{2} - 182 x + 169$

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

$\textcolor{w h i t e}{{\left(5 x + 3\right)}^{3}} = 125 {x}^{3} + 225 {x}^{2} + 135 x + 27$

So:

${\left(5 x + 3\right)}^{3} + {\left(7 x - 13\right)}^{2}$

$= 125 {x}^{3} + 225 {x}^{2} + 135 x + 27 + 49 {x}^{2} - 182 x + 169$

$= 125 {x}^{3} + \left(225 + 49\right) {x}^{2} + \left(135 - 182\right) x + \left(27 + 169\right)$

$= 125 {x}^{3} + 274 {x}^{2} - 47 x + 196$