- Thread starter
- #1

#### PaperStSoap

##### New member

- Jun 26, 2012

- 9

2x

^{3}- 8a

^{2}x + 24x

^{2}+ 72x

so far i got

2x(x

^{2}+ 12x + 36) - 8a

^{2}x

2x(x+6)(x+6) - 8a

^{2}x

don't know what to do from here.

- Thread starter PaperStSoap
- Start date

- Thread starter
- #1

- Jun 26, 2012

- 9

2x

so far i got

2x(x

2x(x+6)(x+6) - 8a

don't know what to do from here.

- Admin
- #2

- Jan 26, 2012

- 4,040

Hi PaperStSoap! Welcome to MHB

2x^{3}- 8a^{2}x + 24x^{2}+ 72x

so far i got

2x(x^{2}+ 12x + 36) - 8a^{2}x

2x(x+6)(x+6) - 8a^{2}x

don't know what to do from here.

You are correct the first step is to factor out 2x from every term, but you didn't include the a^2 term in the factoring. It should be:

\(\displaystyle 2x(x^2-4a^2+12x+36)=2x \left(\left[x^2+12x+36 \right]-4a^2 \right)\)

Now as you noticed part of this immediately factors: \(\displaystyle x^2+12x+36=(x+6)(x+6)=(x+6)^2\)

So now we have \(\displaystyle 2x \left(\left[x+6 \right]^2-4a^2 \right)\)

We can rewrite \(\displaystyle 4a^2\) as \(\displaystyle (2a)^2\)

So simplifying once again we have:

\(\displaystyle 2x \left(\left[x+6 \right]^2-(2a)^2 \right)\)

This is just a difference of squares though! If we let \(\displaystyle c=(x+6)\) and d = \(\displaystyle 2a\) we can think of this as \(\displaystyle 2x(c^2-d^2)=2x(c+d)(c-d)\) So how do we get the final answer from here?

\(\displaystyle 2x \left(x+6+2a \right) \left(x+6-2a \right)\)

Last edited:

- Jan 26, 2012

- 890

Another method:

2x^{3}- 8a^{2}x + 24x^{2}+ 72x

so far i got

2x(x^{2}+ 12x + 36) - 8a^{2}x

2x(x+6)(x+6) - 8a^{2}x

don't know what to do from here.

First rearrange by collecting similar powers of \(x\) and taking out the obvious factoe od \(2x\):

\[2x^3-8a^2x+24x^2+71x=2x^3+24x^2+(71-8a^2)x=2x[x^2+12x+(36-4a^2)]\]

Now the quadratic in the square brackets on the right can be factored by finding its roots using the quadratic formula and constructing the corresponding linear factors.

\[2x^3-8a^2x+24x^2+71x=2x[x^2+12x+(36-4a^2)]=2x(x+6-2a)(x+6+2a)\]

CB