Question

Which expression is equivalent to 64y^18-1000z^6?

Answer 1

For this case we must find an expression equivalent to:$64y ^ {18}-1000z ^ 6$

Then, we take common factor 8:

$8 (64y ^ {18}-125z ^ 6) =$

By definition of power properties we have to:

$(a ^ n) ^ m = a ^ {n * m}$

So:

$8 ((2y ^ 6) ^ 3- (5z ^ 2) ^ 3)$

Since both terms are perfect cubes, we factor using the cube difference formula:

$(a ^ 3-b ^ 3) = (a-b) (a ^ 2 + 2ab + b ^ 2)$

Where:

$a = 2y ^ 6\\b = 5z ^ 2$

So:$8 (2y ^ 6-5z ^ 2) ((2y ^ 6) ^ 2 + 2 (2y ^ 6) (5z ^ 2) + (5z ^ 2) ^ 2) =\\8 (2y ^ 6-5z ^ 2) (4y ^ {12} + 10y ^ 6z ^ 2 + 25z ^ 4)$

Answer:

$8 (2y ^ 6-5z ^ 2) (4y ^ {12} + 10y ^ 6z ^ 2 + 25z ^ 4)$