Question

Factor 6u^2·(2u−5)^2−12u^2·(2u−5)·(u+5)

Answer 1

Start with

$6u^2(2u-5)^2-12u^2(2u-5)(u+5)$

We can factor a 6 from both terms:

$6\big(u^2(2u-5)^2-2u^2(2u-5)(u+5)\big)$

We can also factor $u^2$

$6u^2\big((2u-5)^2-2(2u-5)(u+5)\big)$

Finally, both terms inside the parenthesis contain a factor of $2u-5$

$6u^2(2u-5)\big((2u-5)-2(u+5)\big)$

Finally, we can simplify the terms inside the parenthesis:

$6u^2(2u-5)\big(2u-5-2u-10\big) = 6u^2(2u-5)\big(-15) = -90u^2(2u-5)$