SOLUTION: Hello Please help me solve this problem How do I factorize completely: {{{x^5y-xy}}} and also {{{5a^3-10a^2+3a-6}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello Please help me solve this problem How do I factorize completely: {{{x^5y-xy}}} and also {{{5a^3-10a^2+3a-6}}}       Log On


   

Question 1009757: Hello
Please help me solve this problem
How do I factorize completely:
x%5E5y-xy
and also
5a%5E3-10a%5E2%2B3a-6

Found 3 solutions by MathTherapy, fractalier, MathLover1:
Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Hello
Please help me solve this problem
How do I factorize completely:
x%5E5y-xy
and also
5a%5E3-10a%5E2%2B3a-6
x%5E5y+-+xy

xy%28x%5E4+-+1%29 ----------------- Factoring out GCF, xy

xy%28x%5E2+-+1%29%28x%5E2+%2B+1%29 --------- Factoring difference of 2 squares: x%5E4+-+1 

highlight_green%28xy%28x+-+1%29%28x+%2B+1%29%28x%5E2+%2B+1%29%29 ---- Factoring out difference of 2 squares: x%5E2+-+1



and also 



5a%5E3+-+10a%5E2+%2B+3a+-+6

5a3 - 10a^2 + 3a - 6 ------- Grouping expressions to be factored

5a%5E2%28a+-+2%29+%2B+3%28a+-+2%29

highlight_green%28%285a%5E2+%2B+3%29%28a+-+2%29%29

Answer by fractalier(6550) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E5y-xy...we can write the term x%5E5y as x%5E4%2Axy
so,
x%5E4%2Axy-xy ....both terms have xy in common, so we can factor out xy
xy%28x%5E4-1%29.... write the term x%5E4 as %28x%5E2%29%5E2 and 1 as 1%5E2
xy%28%28x%5E2%29%5E2-1%5E2%29....now we have difference of squares, factor it
xy%28%28x%5E2-1%29%28x%5E2%2B1%29%29....one more time we have difference of squares, factor it
xy%28%28x-1%29%28x%2B1%29%28x%5E2%2B1%29%29



5a%5E3-10a%5E2%2B3a-6....group first two terms together and second two terms together
%285a%5E3-10a%5E2%29%2B%283a-6%29 ...from a group of first two terms factor out 5a%5E2, from a second group factor out 3
5a%5E2%28a-2%29%2B3%28a-2%29
%285a%5E2%2B3%29%28a-2%29