Question

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

Answer 1

2(y+1)(y-3)

Explanation:

(y+4)(y-3)+(y-2)(y-3)
`y^2+y-12+y^2-5y+6`
`2y^2-4y-6`
`2(y+1)(y-3)`

Answer 2

`2y^2-4y-6` or `y^2-2y-3`

Explanation:

FOIL: First-Outside-Inside-Last

• left half
  `(y+4)(y-3)=y(y)+y(-3)+4(y)+4(-3)`
  `=y^2-3y+4y-12`
  `=y^2+y-12`
• right half
  `(y-2)(y-3)=y(y)+y(-3)+(-2)y+(-2)(-3)`
  `=y^2-3y-2y+6`
  `=y^2-5y+6`

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• combine these `\rArr(y^2+y-12)+(y^2-5y+6)`
  simplify `2y^2-4y-6`
  or `y^2-2y-3` if you want to factor out a 2