Factor:
x^4(4) (2x+1)^3 (2x)+(2x+1)^4 (4x^3)
Please help! I cannot figure out how to go about this problem
x^4(4) (2x+1)^3 (2x)+(2x+1)^4 (4x^3)
Collecting factors, we have
8x^5(2x+1)^3 + 4x^3(2x+1)^4
= 4x^3(2x+1)^3 (2x^2+2x+1)
To factor the given expression, you need to identify common factors among the terms and then apply factoring techniques accordingly. Let's break down the given expression step-by-step:
Expression: x^4(4) * (2x+1)^3 * (2x) + (2x+1)^4 * (4x^3)
Step 1: Factor out the common factors from each term.
In the expression, the common factors among the terms are x^4 and (2x+1)^3. Factoring out these common factors, we get:
x^4(4) * (2x+1)^3 * (2x) + (2x+1)^4 * (4x^3)
= x^4 * (2x+1)^3 * [4 * (2x) + (2x+1)]
Simplifying further:
= x^4 * (2x+1)^3 * (8x + 4x + 4 + 2x + 1)
= x^4 * (2x+1)^3 * (14x + 5)
So, the factored form of the given expression is:
x^4 * (2x+1)^3 * (14x + 5)