difference of two squares and difference of two cubes...

Question

Here is the exact question/statement that is needed to be solved...

-Write an expression that can be factored as both a difference of two squares and as a difference of two cubes. Use each method to factor your expression.

Answer 1

x⁶-y⁶ can be factored either as the difference of cubes, giving (x²-y²)(x⁴ + x²y² + y⁴)

 or as the difference of squares, giving (x³-y³)(x³+y³).

Answer 2

x⁶-y⁶

(x²)³-(y²)³=(x²-y²)([x²]²+x²y²+[y²]²)

 

(x³)²-(y³)²=(x³-y³)(x³+y³)