Question

which expression is equivalent to 36a - 27?
9(4a - 3)
3(18a - 9)
9(4a - 27)
3(12a - 6)

Explanation:

Step1: Factor out GCF of 36a - 27

The greatest common factor (GCF) of 36a and 27 is 9. So, we factor 9 out of the expression.
$$36a - 27 = 9\times4a - 9\times3$$
Using the distributive property \(ab - ac = a(b - c)\), we get:
$$9(4a - 3)$$

Step2: Check other options (optional but for verification)

• For \(3(18a - 9)\): Factoring out 3, we get \(3\times18a - 3\times9 = 54a - 27

eq36a - 27\).

• For \(9(4a - 27)\): Expanding, we get \(9\times4a - 9\times27 = 36a - 243

eq36a - 27\).

• For \(3(12a - 6)\): Expanding, we get \(3\times12a - 3\times6 = 36a - 18

eq36a - 27\).

Answer:

A. \(9(4a - 3)\)