SOLUTION: Please help me factor this: {{{ x^4(4)(2x+1)^3(2x)+(2x+1)^4(4x^3) }}} The book says {{{ x^4(4)(2x+1)^3(2x)+(2x+1)^4(4x^3) = 2x^3(2x+1)^3 (4x^2+2(2x+1)) }}} = {{{ 2x^3(2x+1)^

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me factor this: {{{ x^4(4)(2x+1)^3(2x)+(2x+1)^4(4x^3) }}} The book says {{{ x^4(4)(2x+1)^3(2x)+(2x+1)^4(4x^3) = 2x^3(2x+1)^3 (4x^2+2(2x+1)) }}} = {{{ 2x^3(2x+1)^      Log On


   

Question 823788: Please help me factor this: +x%5E4%284%29%282x%2B1%29%5E3%282x%29%2B%282x%2B1%29%5E4%284x%5E3%29+
The book says
= +2x%5E3%282x%2B1%29%5E3%284x%5E2%2B4x%2B2%29+
= +4x%5E3%282x%2B1%29%5E3%282x%5E2%2B2x%2B1%29+
In the first line, I understand how +2x%5E3%282x%2B1%29%5E3+ and +%282x%2B1%29+ are factored, but what is really confusing me is how +4x%5E2%2B2+ are factored. The lines following I also understand.
Thanks.
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E4%284%29%282x%2B1%29%5E3%282x%29%2B%282x%2B1%29%5E4%284x%5E3%29+
I think it will be easier to understand if we simplify a little before factoring. The first term. +x%5E4%284%29%282x%2B1%29%5E3%282x%29, can simplify a little if we multiply the x%5E4, the 4 and the 2x together:
+8x%5E5%282x%2B1%29%5E3%2B%282x%2B1%29%5E4%284x%5E3%29+

Now we can factor a 4 from the 8 and the 4, a x%5E3 from the x%5E5 and the x%5E3, and a %282x%2B1%29%5E3 from the %282x%2B1%29%5E3 and the %282x%2B1%29%5E4:
4x%5E3%282x%2B1%29%5E3%282x%5E2+%2A+1+%2B+1%2A1%2A%282x%2B1%29%29
Now we just simplify the second factor:
4x%5E3%282x%2B1%29%5E3%282x%5E2+%2B+2x%2B1%29