6.10 Special Products

Objectives: •To square a binomial•To find products of the form (a + b)(a – b)

Frameworks: 10.P.3

How do we square a binomial?

(x + 3)2 = (x + 3)(x + 3)FOIL: = x2 + 3x + 3x + 9 = x2 + 6x + 9 Square of a sum: (first term)2 + 2(first x last) + (last term)2

Squaring a difference:

(3x - 5)2 = (3x - 5)(3x - 5)FOIL: = 9x2 - 15x - 15x + 25 = 9x2 - 30x + 25 Square of a difference: (first term)2 - 2(first x last) + (last term)2

Notice

(x + 3)2 ≠ x2 + 9(3x – 5)2 ≠ 9x2 + 25

When you square a binomial the product always contains three terms.

Square of a Binomial

(a + b)2 = a2 + 2ab + b2

(a - b)2 = a2 - 2ab + b2

Try some:

(x – 8)(x - 8)

(2y + 1)2

(3x - 2)2

(5a + 1)2

What about multiplying the sum and difference of the same 2 terms?

(x + 6)(x - 6)FOIL: = x2 - 6x + 6x - 36 = x2 - 36

(first term)2 - (last term)2

Product of (a + b)(a – b): a2 - b2

Try some:

(c – 1)(c + 1)

(4x – 3)(4x + 3)

(3x + 2)(3x – 2)

And now for something really fun:

(x – 5)2 = (x - 8)(x + 8) x2 – 10x + 25 = x2 – 64- x2 = -x2

– 10x + 25 = – 64 - 25 - 25 - 10 x = - 89 x = 8.9

Try another fun one:

(x – 4)2 = (x - 8)(x + 2)

Turn to page 234

Do 1-4