Question

write an equivalent expression
3x - 27
select all that apply.
a. 3(3x - 9)
b. 3(x - 27)
c. (x - 9)3
d. 3(x - 9)

Explanation:

Step1: Factor out 3 from \(3x - 27\)

Find the greatest common factor (GCF) of \(3x\) and \(27\), which is 3. So, \(3x - 27 = 3(x - 9)\).

Step2: Analyze Option A

Expand \(3(3x - 9)\): \(3\times3x - 3\times9 = 9x - 27\), not equal to \(3x - 27\). So A is incorrect.

Step3: Analyze Option B

Expand \(3(x - 27)\): \(3x - 81\), not equal to \(3x - 27\). So B is incorrect.

Step4: Analyze Option C

\((x - 9)3\) is the same as \(3(x - 9)\) (multiplication is commutative), which is equal to \(3x - 27\) when expanded. So C is correct.

Step5: Analyze Option D

\(3(x - 9)\) expands to \(3x - 27\), which is equal to the original expression. So D is correct.

Answer:

C. \((x - 9)3\), D. \(3(x - 9)\)