Special Products

Special Polynomial Multiplying

Remember: When multiplying polynomials, make sure EVERY MEMBER of the first group multiplies EVERY MEMBER of the second group!

(3x + 5)(2x + 5)

PRACTICE!!

(x – 3)(x + 5) x

2

+

5x

+

-3x

+

x + 2x -15 2

-15

Remember:

3

2

=3•3 x

2

=x•x

2

=

2

=

• A polynomial can be treated just like it is a regular number.

2

(x + 2)

=

(x + 2) ● (x + 2)

(x + 2)

2

This means “(x+2) times itself !”

(x + 2)(x + 2)

Then solve it normally!

(x + 2)(x + 2)

Try These

1. (x – 1)

2

2. (2x + 1)2

= (x – 1)(x – 1)

Another “Special Product” involves the same terms, but with different signs.

(x + 3)(x – 3)

Try This First

3. (x + 3)(x – 3)

Notice that when we multiply this type of problem, the middle term always cancels out.

(x – 4)(x + 4) x + 4x + -4x + -16 2

x – 16 2

• These special products are called Difference of Squares See if you can do them mentally:

(x + 5)(x – 5)

Try These Mentally 4. (2x – 5)(2x + 5) 5. (x – 10)(x + 10) 6. (3x + 3)(3x – 3)