# How do you simplify (7y -x)^2?

Jan 25, 2017

$49 {y}^{2} + {x}^{2} - 14 x y$

#### Explanation:

It is a binomial squared:

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

Jan 25, 2017

See below.

#### Explanation:

This is a binomial so we can make use of the standard formula

${\left(\textcolor{red}{\text{a"-color(blue)"b}}\right)}^{2}$ $=$ ${\textcolor{red}{\text{a}}}^{2}$ - $2 \textcolor{red}{\text{a"color(blue)"b}}$ + ${\textcolor{b l u e}{\text{b}}}^{2}$

For our purposes, color(red)("a"=7y and color(blue)("b"=x . Putting the values in the above given equation we obtain:

${\left(7 y - x\right)}^{2}$ = $49 {y}^{2} - 2 \cdot 7 y \cdot x + {x}^{2}$

$\implies$ ${\left(7 y - x\right)}^{2}$ = $49 {y}^{2} - 14 x y + {x}^{2}$

Jan 25, 2017

$49 {y}^{2} - 14 y x + {x}^{2}$

#### Explanation:

${\left(7 y - x\right)}^{2}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$7 y - x$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$7 y - x$

$\textcolor{w h i t e}{a a a a a a a a a a a}$$- - -$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$49 {y}^{2} - 7 y x$

$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$- 7 y x + {x}^{2}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- - - - - -$

$\textcolor{w h i t e}{a a a a a a a a a a a a}$$49 {y}^{2} - 14 y x + {x}^{2}$