Question

How do you factor the trinomial `3(a + b)^2 - 18(a + b) - 216`?

Answer 1

`3(a+b-12)(a+b+6)`

Explanation:

`"using the substitution "x=a+b`

`rArr3(a+b)^2-18(a+b)-216`

`=3x^2-18x-216`

`"take out a "color(blue)"common factor "3`

`=3(x^2-6x-72)`

`"the factors of - 72 which sum to - 6 are - 12 and + 6"`

`=3(x-12)(x+6)`

`"change x back to "a+b`

`=3(a+b-12)(a+b+6)`