Algebra

10.3 Special Products of Polynomials

Multiply. We can find a shortcut.

(x + y) (x – y)

x² - xy + xy - y2

= x² - y2Shortcut: Square the first term and subtract the square of the second term.

This is a “DTS,” the difference of two squares.

This is the sum and difference pattern.

Multiply. Use the shortcut.

(3x + 8y) (3x – 8y)

= (3x)² - (8y)2

Shortcut: Square the first term and subtract the square of the second term.

= 9x² - 64y2

Try these!

(x + 7) (x – 7)

(4t + 1)(4t – 1)

(9x – 5y)(9x + 5y)

(-3x + 5)(-3x – 5)

x²- 49

16t²- 1

81x²- 25y²

9x²- 25

Multiply. We can find a shortcut.

(x + y) (x + y)

x² + xy + xy + y2

= x² + 2xy + y2Shortcut: Square the first term, add twicethe product of both terms and add the square of the second term.

This is a “Perfect Square Trinomial.”

(x + y)2

This is the square of a binomial pattern.

Multiply. Use the shortcut.

(4x + 5)2

= (4x)² + 2(4x●5) + (5)2

Shortcut:

= 16x² + 40x + 25

x² + 2xy + y2

Try these!

(x + 3)2

(5m + 8)2

(2x + 4y)2

(-4x + 7)2

x² + 6x + 9

25m² + 80m + 64

4x² + 16xy + 16y²

16x²- 56x + 49

Multiply. We can find a shortcut.

(x – y) (x – y)

x² - xy - xy + y2

= x² - 2xy + y2

This is a “Perfect Square Trinomial.”

(x – y)2

This is the square of a binomial pattern.

Multiply. Use the shortcut.

(3x - 7)2

Shortcut:

= 9x² - 42x + 49

x² - 2xy + y2

Try these!

(x – 7)2

(3p - 4)2

(4x - 6y)2

x² - 14x + 49

9p² - 24p + 16

16x² - 48xy + 36y²

A mixture of all three!

(2x + 3)2

(2p - 4) (2p + 4)

(2x - y)2

4x² + 12x + 9

4p² - 16

4x² - 4xy + y²

HW

• P. 593-595 (15-42, 63-68)