SOLUTION: Factor the polynomial: (v-2u)^2-(2u-v)(u+2v)-2v+4u All that I know is that (2u-v)=-(v-2u). I'd really appreciate your help! Thank you!

Algebra ->  Equations -> SOLUTION: Factor the polynomial: (v-2u)^2-(2u-v)(u+2v)-2v+4u All that I know is that (2u-v)=-(v-2u). I'd really appreciate your help! Thank you!      Log On


   

Question 1126153: Factor the polynomial:
(v-2u)^2-(2u-v)(u+2v)-2v+4u
All that I know is that (2u-v)=-(v-2u). I'd really appreciate your help! Thank you!
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+%28v-2u%29%5E2-%282u-v%29%28u%2B2v%29-2v%2B4u+
= +%28v-2u%29%5E2+%2B+%28%28v-2u%29%28u%2B2v%29%29+%2B+%28-2%29%28v-2u%29+

Factoring out the common +%28v-2u%29+ :
= +%28v-2u%29++%28+%28v-2u%29+%2B+%28u%2B2v%29+-2++%29++
= +highlight+%28+%28v-2u%29+%28+3v-u-2+%29%29++
which is equivalent to ++highlight+%28+%282u-v%29+%28+u-3v%2B2+%29%29++

I encourage you to multiply this result out, and the original expression as well. Then compare them to prove to yourself that they are indeed equal.