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

Note that

and

Then

Use the formula for difference of the squares:

Thus,

correct choice is D.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb