Question

Which expression is equivalent to 36x2 − 25? (18x)2 (−5)2 (18x)2 − (5)2 (6x)2 (−5)2 (6x)2 − (5)2

Answer 1

Note that

`36=6^2,\\ 25=5^2`

and

`a^2\cdot b^2=(ab)^2`

Then

`36x^2 - 25=6^2\cdot x^2-5^2=(6x)^2-5^2.`

Use the formula for difference of the squares:

`a^2-b^2=(a-b)(a+b).`

Thus,

`36x^2 - 25=(6x)^2-5^2=(6x-5)(6x+5).`

Answer: correct choice is D.