# Factoring

• Sep 27th 2009, 06:38 PM
WilliamR
Factoring
I believe i know the answer this this one, but i just want to make sure.
Could someone tell me the answer to the following:

Factor the difference of two sqaures,
25 - (z+5)²
Also, this one, i am having a hard time finding the answer to:
Completely factor the expression,
5(3-4x)² - 8(3-4x)(5x-1)

Thanks :)
• Sep 27th 2009, 06:44 PM
VonNemo19
Quote:

Originally Posted by WilliamR
I believe i know the answer this this one, but i just want to make sure.
Could someone tell me the answer to the following:

Factor the difference of two sqaures,
25 - (z+5)²
Also, this one, i am having a hard time finding the answer to:
Completely factor the expression,
5(3-4x)² - 8(3-4x)(5x-1)

Thanks :)

In the first, let z+5=a. This makes the problem look a little less distracting. We can always replace the z+5 after the end. So... How would you factor...

\$\displaystyle 25-a^2\$

It would look like this

\$\displaystyle (5+a)(5-a)\$

now if I put z+5 back in...

\$\displaystyle [5+(z+5)][5-(z+5)]\$

And you can simplify further.

In the second problem, try putting a=3x-4, and b= 5x-1. Then factor and replace like the last problem.
• Sep 27th 2009, 07:06 PM
WilliamR
I am still not sure about the answer the the second problem (Rock)
• Sep 27th 2009, 07:15 PM
5(3-4x)² - 8(3-4x)(5x-1)
(3 - 4x) [ 5(3-4x) - 8(5x-1)] ... can you finish?
• Sep 27th 2009, 07:16 PM
VonNemo19
Quote:

Originally Posted by WilliamR
I am still not sure about the answer the the second problem (Rock)

Can you factor

\$\displaystyle 5a^2-8ab\$ ?
• Sep 27th 2009, 07:26 PM
WilliamR
Quote:

Originally Posted by VonNemo19
Can you factor

\$\displaystyle 5a^2-8ab\$ ?

a(5a-8b)

Quote:

5(3-4x)² - 8(3-4x)(5x-1)
(3 - 4x) [ 5(3-4x) - 8(5x-1)] ... can you finish?

Erm....240x² -272x+69....?
• Sep 27th 2009, 07:28 PM

(3-4x) [ 5(3-4x) - 8(5x-1)]
(3-4x) [ (15 - 20x) - 40x + 8)]
(3-4x) [ -60x + 23 ]

and we are done factoring.
• Sep 27th 2009, 07:30 PM
WilliamR
Quote:

(3-4x) [ 5(3-4x) - 8(5x-1)]
(3-4x) [ (15 - 20x) - 40x + 8)]
(3-4x) [ -60x + 23 ]

and we are done factoring.

I see now, that is clear, thank you .
• Sep 27th 2009, 07:41 PM
VonNemo19
Now substitute back for a and b.

The point that I'm trying to make here is that factors can be a distraction if they contain more than one term like (z+5). But if you look at it like the way that I've showed you, you will become really good really fast.

Sometimes its better not to just give someone a solution....

But actually teach them something.(Hi)
• Sep 27th 2009, 08:17 PM
pacman
VonNemo19, i agree with you. That is what MATH HELPER FORUM intends to, guiding them. Voila!(Rock)