SOLUTION: can these trinomials be faxctored and if so how? i am totally lost u^3 – 125v^3 -4w3 – 16w2 + 20w -36a^2b + 21ab^2 – 3b^3 x^2 – 5xz -24z^2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can these trinomials be faxctored and if so how? i am totally lost u^3 – 125v^3 -4w3 – 16w2 + 20w -36a^2b + 21ab^2 – 3b^3 x^2 – 5xz -24z^2       Log On


   

Question 275586: can these trinomials be faxctored and if so how? i am totally lost
u^3 – 125v^3
-4w3 – 16w2 + 20w
-36a^2b + 21ab^2 – 3b^3
x^2 – 5xz -24z^2
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
1) u%5E3-125v%5E3 Do you recognize this as the difference of two cubes?
%28u%29%5E3-%285v%29%5E3
The difference of two cubes can be factored thus:
A%5E3-B%5E3+=+%28A-B%29%28A%5E2%2BAB%2BB%5E2%29 so...
highlight%28u%5E3-125v%5E3+=+%28u-5v%29%28u%5E2%2B5uv%2B25v%5E2%29%29
2) -4w%5E3-16w%5E2%2B20w First factor -4w
-4w%28w%5E2%2B4w-5%29 Now factor the trinomial in parentheses.
-4w%28w-1%29%28w%2B5%29 so...
highlight%28-4w%5E3-16w%5E2%2B20w+=+-4w%28w-1%29%28w%2B5%29%29
3) -36a%5E2b%2B21ab%5E2-3b%5E3 First factor -3b.
-3b%2812a%5E2-7ab%2Bb%5E2%29 Now factor the trinomial in parentheses.
-3b%283a-b%29%284a-b%29 so...
highlight%28-36a%5E2b%2B21ab%5E2-3b%5E3+=+-3b%283a-b%29%284a-b%29%29
4) highlight%28x%5E2-5xz-24z%5E2+=+%28x%2B3z%29%28x-8z%29%29