# How do you expand and simplify (y+4)(y-3)+(y-2)(y-3)?

Dec 11, 2016

2(y+1)(y-3)

#### Explanation:

(y+4)(y-3)+(y-2)(y-3)
${y}^{2} + y - 12 + {y}^{2} - 5 y + 6$
$2 {y}^{2} - 4 y - 6$
$2 \left(y + 1\right) \left(y - 3\right)$

Dec 11, 2016

$2 {y}^{2} - 4 y - 6$ or ${y}^{2} - 2 y - 3$

#### Explanation:

FOIL: First-Outside-Inside-Last

• left half
$\left(y + 4\right) \left(y - 3\right) = y \left(y\right) + y \left(- 3\right) + 4 \left(y\right) + 4 \left(- 3\right)$
$= {y}^{2} - 3 y + 4 y - 12$
$= {y}^{2} + y - 12$
• right half
$\left(y - 2\right) \left(y - 3\right) = y \left(y\right) + y \left(- 3\right) + \left(- 2\right) y + \left(- 2\right) \left(- 3\right)$
$= {y}^{2} - 3 y - 2 y + 6$
$= {y}^{2} - 5 y + 6$

• combine these $\setminus \Rightarrow \left({y}^{2} + y - 12\right) + \left({y}^{2} - 5 y + 6\right)$
simplify $2 {y}^{2} - 4 y - 6$
or ${y}^{2} - 2 y - 3$ if you want to factor out a 2