# How do you combine like terms in (5- x ) ( 5+ x ) + ( x - 5) ^ { 2} + ( 2x - 10) ( x + 3)?

Jul 27, 2018

$2 {x}^{2} - 14 x + 20$

#### Explanation:

$\left(5 - x\right) \left(5 + x\right) + {\left(x - 5\right)}^{2} + \left(2 x - 10\right) \left(x + 3\right)$ can be separated into 3 parts:

• $\left(5 - x\right) \left(5 + x\right) = 25 - {x}^{2}$ (difference of 2 squares)

• ${\left(x - 5\right)}^{2} = {x}^{2} - 10 x + 25$ (perfect squares)

• $\left(2 x - 10\right) \left(x + 3\right) = 2 {x}^{2} - 4 x - 30$

$\left(5 - x\right) \left(5 + x\right) + {\left(x - 5\right)}^{2} + \left(2 x - 10\right) \left(x + 3\right)$
$= 25 - {x}^{2} + {x}^{2} - 10 x + 25 + 2 {x}^{2} - 4 x - 30$
$= 25 \cancel{- {x}^{2} + {x}^{2}} - 10 x + 25 + 2 {x}^{2} - 4 x - 30$
$= 2 {x}^{2} - 14 x + 20$

Jul 27, 2018

$2 {x}^{2} - 14 x + 20$

#### Explanation:

$\left(5 - x\right) \left(5 + x\right) + {\left(x - 5\right)}^{2} + \left(2 x - 10\right) \left(x + 3\right)$

=$25 - {x}^{2} + {x}^{2} - 10 x + 25 + 2 {x}^{2} - 4 x - 30$

=$2 {x}^{2} - 14 x + 20$