Question

Factor 9x 6 – 16y 6 completely.

First factor each term.
9x 6 = (__)2
16y 6 = (__)2

Then use a2 – b2 = (a – b)(a + b). Show your work.

9x 6 – 16y 6 =

Answer 1

Please use the symbol " ^ " to denote exponentiation:  9x^6 = (___)^2.

Note that 9x^6 = 3^2*(x^3)^2.  Thus,

9x^6 = (___)^2 becomes (3x^3)^2.

Then    9x^6 – 16y^6 = (3x^3)^2 - (4y^3)^2 = ((3x^3) - (4y^3))[(3x^3) +(4y^3)]