What is the Factored Form of the Derivative Using Product Rule?

[cataschok]

Homework Statement

use product rule to find the derivative of g(x)=(2x+1)^2(x-7)^3

Homework Equations

i've applied chain rule and product rule to get...

The Attempt at a Solution

4(2x+1)(x-7)^3+3(2x+1)^2(x-7)^2

i need to factor out to get the following..
5(x-7)^2(2x-5)(2x+1)
That's the final answer from the book. But the steps to get there... I'm lost. Can anyone help me out on getting it to the factored form?

 

[Mark44]

Homework Statement

use product rule to find the derivative of g(x)=(2x+1)^2(x-7)^3

Homework Equations

i've applied chain rule and product rule to get...

The Attempt at a Solution

4(2x+1)(x-7)^3+3(2x+1)^2(x-7)^2

i need to factor out to get the following..
5(x-7)^2(2x-5)(2x+1)
That's the final answer from the book. But the steps to get there... I'm lost. Can anyone help me out on getting it to the factored form?

Look for factors that are common to both terms.
4(2x+1)(x-7)³+3(2x+1)²(x-7)^2
= (2x+1)(x - 7)²[4(x - 7) + 3(2x + 1)]

Now combine the terms in the brackets and pull out the common factor there, and you'll have what you need.

 

[cataschok]

thank you kind sir, you have saved me many hours of frustration!