1. Special Products

The following special products come from multiplying out the brackets. You'll need these often, so it's worth knowing them well.

a(x + y) = ax + ay

(x + y)(xy) = x2y2 (Difference of 2 squares)

(x + y)2 = x2 + 2xy + y2 (Square of a sum)

(xy)2 = x2 − 2xy + y2 (Square of a difference)

Examples using the special products

Example 1: Multiply out 2x(a − 3)

Example 2: Multiply `(7s + 2t)(7s − 2t)`

Example 3: Multiply (12 + 5ab)(12 − 5ab)

Example 4: Expand (5a + 2b)2

Example 5: Expand (q − 6)2

Example 6: Expand (8x y)(3x + 4y)

Example 7: Expand (x + 2 + 3y)2

Special Products involving Cubes

The following products are just the result of multiplying out the brackets.

(x + y)3 = x3 + 3x2y + 3xy2 + y3 (Cube of a sum)

(x y)3 = x3 − 3x2y + 3xy2 y3 (Cube of a difference)

(x + y)(x2xy + y2) = x3 + y3 (Sum of 2 cubes)

(xy)(x2 + xy + y2) = x3 y3 (Difference of 2 cubes)

These are also worth knowing well enough so you recognize the form, and the differences between each of them. (Why? Because it's easier than multiplying out the brackets and it helps us solve more complex algebra problems later.)

Example: Expand `(2s + 3)^3`

Exercises

Expand:

(1) (s + 2t)(s − 2t)

(2) (i1 + 3)2

(3) (3x + 10y)2

(4) (3p − 4q)2

Didn't find what you are looking for on this page? Try search:

Online Algebra Solver

This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)

Ready for a break?

 

Play a math game.

(Well, not really a math game, but each game was made using math...)

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!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

Share IntMath!

Short URL for this Page

Save typing! You can use this URL to reach this page:

intmath.com/specpro

Algebra Lessons on DVD

 

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

More info: Algebra videos

Loading...
Loading...