Question: Factor by grouping. 36b + 4h + 9bq + hq 36b + 4h + 9bq + hq = \boxed{\phantom{Type your answer…

Factor by grouping.

36b + 4h + 9bq + hq

36b + 4h + 9bq + hq = \boxed{\phantom{Type your answer in factored form.}}

Solution

To factor the expression by grouping, follow these steps: Group the terms: \[ (36b + 4h) + (9bq + hq) \] Factor out the common factor from each group: In the first group \((36b + 4h)\), the common factor is 4: \[ 4(9b + h) \] In the second group \((9bq + hq)\), the common factor is \(q\): \[ q(9b + h) \] Now combine these factored expressions: \[ 4(9b + h) + q(9b + h) \] Factor out the common binomial \((9b + h)\): \[ (9b + h)(4 + q) \] Thus, the factored form is: \[ (9b + h)(4 + q) \]