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)`