How do you factor the trinomial $(a + b)^2 - 9(a + b) - 36$ ?

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Answer 1 · 2015-11-29T02:45:34

$(a+b)^2-9(a+b)-36=(a+b+3)(a+b-12)$

$(a+b)^2-9(a+b)-36$ is a quadratic equation in the form $ax^2+bx+c$ , where $a=1, b=-9, and c=-36$ .

For the time being, let $(a+b)=x$ . After factoring with $x$ , $(a+b)$ will be substituted into the factors.

$x^2-9x-36$ . Find two numbers that when added equal $-9$ and when multiplied equal $-36$ . The numbers $3$ and $-12$ meet the criteria.

Rewrite the expression.

$(x+3)(x-12)$

Now substitute $(a+b)$ back into the expression in place of $x$ .

$(a+b)^2-9(a+b)-36=((a+b)+3)((a+b)-12)=(a+b+3)(a+b-12)$

How do you factor the trinomial (a + b)^2 - 9(a + b) - 36 (a + b)^2 - 9(a + b) - 36?