# Factoring / Simplifying Polynomials

#### Islandchild

##### New member
I have just recently started upgrading my math in University and am coming to some stand stills.....help?

(3x-4y)(2a+3b)

How can you simplify this equation if there are no common terms?
How would you complete this equation step by step?

#### wjm11

##### Senior Member
(3x-4y)(2a+3b)

How can you simplify this equation if there are no common terms?
How would you complete this equation step by step?
First of all, some terminology: it is not an equation; there is no equal sign. It is a mathematical expression. You can’t “solve” it, but you can “expand” it: multiply each term in the second part by each term in the first part:

(3x-4y)(2a+3b)
= (3x)(2a) + (3x)(3b) + (-4y)(2a) + (-4y)(3b)
= 6ax + 9bx – 8ay – 12by

Hope that helps.

#### Islandchild

##### New member
Hi!
Thanks wjm11 for the info! Wierd thing is I actually expanded the expression excactly the same as you did. It just didn't look right so I thought I would double check.

Any chance the expressions below are just as easy to factor?

1) 125x^3 - 8y^3

2) 2(5x-1)^3 - (5x-1)^2

#### mmm4444bot

##### Super Moderator
Staff member
Islandchild said:
Any chance the expressions below are just as easy to factor?

1) 125x^3 - 8y^3

This one is easy, if you recognize that it's a difference of cubes.

(Both 125 and 8 are cubes.)

There are special factoring formulas for both a sum of cubes and a difference of cubes.

2) 2(5x-1)^3 - (5x-1)^2

Hint: Factor out a factor of (5x - 1)^2 from each term, then simplify.

In other words, fill in the blanks below and then simplify what's inside the square brackets.

(5x - 1)^2 * [ ____ - ____ ]

#### Islandchild

##### New member
Hi!
Hey thanks so much! I feel silly, but when I've been looking at questions for hours on end things start to seem more complicated then they really are

#### Rodsh

##### New member
Factoring

Question:

Looking for two perfect numbers, the factors of which equals the respective number . . . ??

If 4 is one answer (I think), what would the other or another?

Thanks -

#### mmm4444bot

##### Super Moderator
Staff member
Rodsh said:
Looking for two perfect numbers, the factors of which equals the respective number
Do you mean "the sum of the factors of which equals the respective number"?