How do I factor (ab+3a-5b-15) by grouping?
ab + 3a - 5b - 15
= a(b+3) - 5(b+3_
= (b+3)(a-5)
expand to verify
ab+5b+3a+15
To factor the expression (ab+3a-5b-15) by grouping, we need to rearrange the terms and group them in pairs. Here's how you can do it step-by-step:
Step 1: Group the terms in pairs.
(ab + 3a) - (5b + 15)
Step 2: Factor out the greatest common factor from each pair.
a(b + 3) - 5(b + 3)
Step 3: Notice that both pairs have a common binomial factor (b + 3). Factor out the common binomial factor.
(b + 3)(a - 5)
So, by grouping, the factored form of the expression (ab+3a-5b-15) is (b + 3)(a - 5).