Question

factor the trinomial
b² + 10bz + 16z²
b² + 10bz + 16z² = \square

Explanation:

Step1: Identify target pair

Find two numbers that multiply to $16$ and add to $10$. These numbers are $2$ and $8$, since $2 \times 8 = 16$ and $2 + 8 = 10$.

Step2: Split the middle term

Rewrite the trinomial by splitting the middle term using the pair from Step1:
$b^2 + 2bz + 8bz + 16z^2$

Step3: Factor by grouping

Group the first two and last two terms, then factor out the common factor from each group:
$b(b + 2z) + 8z(b + 2z)$

Step4: Factor out the binomial

Factor out the common binomial factor $(b + 2z)$:
$(b + 2z)(b + 8z)$

Answer:

$(b + 2z)(b + 8z)$