Question

The area of a rectangle is represented by the expression 16m - 24. Which expression shows a factored version of the Area, one that shows the length and the width.

A | 8(2m+3)
B | 8(2+3m)
C | 8(2-3m)
D | 8(2m-3)

Answer 1

The espression 8(2m - 3) shows the length and the width of the rectangle ⇒ D

Explanation:

Let us find the greatest common factor of 16 and 24

∵ 16 = 1 × 16, 2 × 8, 4 × 4

∴ The factors of 16 are 1, 2, 4, 8, 16

∵ 24 = 1 × 24, 2 × 12, 3 × 8, 4 × 6

∴ The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

→ Find the common factors of 16 and 24

∵ The common factor of 16 and 24 are 1, 2, 4, 8

∵ The greatest one is 8

∴ The greatest common factor of 16 and 24 is 8

→ Take 8 as a common factor from 16m and 24

∵ 16m ÷ 8 = 2m

∵ 24 ÷ 8 = 3

∴ 16m - 24 = 8(2m - 3)

∴ The espression 8(2m - 3) shows the length and the width of

the rectangle