# 2. Multiplication of Algebraic Expressions

Einstein's famous equation involves multiplying algebraic terms

When we multiply algebraic expressions, we need to remember the Index Laws from the Numbers chapter.

Let's see how algebra multiplication works with a series of examples.

## Example 1

Multiply *x*^{3}(*x*^{4} + 5*a*)

Answer

We expand this out using the distributive law:

x^{3}(x^{4}+ 5a)=

x^{7}+ 5ax^{3}

We cannot simplify this answer any further. We present our answer in alphabetical order since it makes it easier to read when the problems become more involved.

Easy to understand math videos:

MathTutorDVD.com

## Example 2

Multiply (*x* +
5)(*a* − 6)

Answer

We multiply this out as follows. We take each term of the first bracket and multiply them by the second bracket. Then we expand out the result.

(

x+ 5)(a− 6)=

x(a− 6) + 5(a− 6)=

ax− 6x+ 5a− 30

We cannot do any more with this answer. There are no like terms, so we cannot simplify it in any way.

Get the Daily Math Tweet!

IntMath on Twitter

## Example 3

Multiply (2*x* +
3)(*x*^{2} − *x* − 5)

Answer

We take the 2 terms of the first bracket and multiply both of them by the second bracket.

(2*x* + 3)(*x*^{2}− *x* − 5)

= (2*x*)(*x*^{2} − *x* − 5) +
(3)(*x*^{2} − *x* − 5)

= (2*x*^{3} − 2*x*^{2} − 10*x*) + (3*x*^{2} − 3*x* − 15)

= 2*x*^{3} + *x*^{2} −
13*x* − 15

This time we could collect together some like terms. There was:

−2

x^{2}+ 3x^{2}=x^{2}

and

−10

x− 3x= −13x

Please support IntMath!

## Example 4

Multiply `(x - 3)^2`

Answer

(*x* − 3)^{2}

= (*x* − 3)(*x* − 3)

= *x*(*x* − 3) − 3(*x*
− 3)

= *x*^{2} − 3*x* −
3*x* + 9

= *x*^{2} − 6*x* + 9

Easy to understand math videos:

MathTutorDVD.com

## Important Note:

`(x - 3)^2`

is NOT equal to

`x^2 - 9`

Please take note of this! Many students confuse this idea and it's not surprising because sometimes the way we write math is not consistent. (See also Towards more meaningful math notation for a discussion on this issue.)

## Example 5

Simplify 5*x*[−4 + 10(*x* − *y*)] + 7*x*

Answer

5*x*[−4 + 10(*x* − *y*)] +
7*x*

= 5*x*[−4 + 10*x* − 10*y*] +
7*x*

= −20*x* + 50*x*^{2} − 50*xy* +
7*x*

= −13*x* + 50*x*^{2} − 50*xy*

## Example 6

Simplify (*p* − 1)(*c* − 1) + 2

Answer

*p*(*c* − 1) − 1(*c* − 1) + 2

= *pc* − *p* − *c* + 1 + 2

= *pc* − *p* − *c* + 3

Get the Daily Math Tweet!

IntMath on Twitter

### Search IntMath, blog and Forum

### Online Algebra Solver

This algebra solver can solve a wide range of math problems.

Go to: Online algebra solver

### Algebra Lessons on DVD

Math videos by MathTutorDVD.com

Easy to understand algebra lessons on DVD. See samples before you commit.

More info: Algebra videos

### The IntMath Newsletter

Sign up for the free **IntMath Newsletter**. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!