Question

write an equivalent expression.
3b + 21

select all that apply.
a. 3(3b + 7)
b. (b + 7)3
c. 3(b + 21)
d. 3(b + 7)

Explanation:

Step1: Factor out 3 from \(3b + 21\)

To factor the expression \(3b + 21\), we look for the greatest common factor (GCF) of the two terms. The GCF of \(3b\) and \(21\) is 3. So we factor out 3: \(3b + 21 = 3(b + 7)\).

Step2: Analyze Option B

Option B is \((b + 7)3\). Multiplication is commutative, so \((b + 7)3 = 3(b + 7)\), which is equivalent to the factored form of \(3b + 21\).

Step3: Analyze Option D

Option D is \(3(b + 7)\), which is exactly the factored form we found in Step 1, so it is equivalent.

Step4: Analyze Option A

Option A is \(3(3b + 7)\). Let's expand it: \(3\times3b + 3\times7 = 9b + 21\), which is not equal to \(3b + 21\), so it is not equivalent.

Step5: Analyze Option C

Option C is \(3(b + 21)\). Expanding it: \(3\times b + 3\times21 = 3b + 63\), which is not equal to \(3b + 21\), so it is not equivalent.

Answer:

B. \((b + 7)3\), D. \(3(b + 7)\)