Algebra 10 3 Special Products of Polynomials Multiply

Algebra 10. 3 Special Products of Polynomials

Multiply. We can find a shortcut. (x + y) (x – y) This is the sum and difference pattern. x² - = x² xy - y 2 + xy - y 2 Shortcut: Square the first term and subtract the square of the second term. This is a “DTS, ” the difference of two squares.

Multiply. Use the shortcut. (3 x + 8 y) (3 x – 8 y) Shortcut: Square the first term and subtract the square of the second term. = (3 x)² - (8 y)2 = 9 x² - 64 y 2

Try these! (x + 7) (x – 7) x²- 49 (4 t + 1)(4 t – 1) 16 t²- 1 (9 x – 5 y)(9 x + 5 y) 81 x²- 25 y² (-3 x + 5)(-3 x – 5) 9 x²- 25

Multiply. We can find a shortcut. (x + 2 y) This is the square of a binomial pattern. (x + y) x² = x² + xy + + 2 xy + y 2 This is a “Perfect Square Trinomial. ” xy + y 2 Shortcut: Square the first term, add twice the product of both terms and add the square of the second term.

Multiply. Use the shortcut. (4 x + 5)2 Shortcut: = x² + 2 xy + y 2 (4 x)² + 2(4 x 5) + (5)2 ● = 16 x² + 40 x + 25

Try these! (x + 3)2 x² + 6 x + 9 (5 m + 8)2 25 m² + 80 m + 64 (2 x + 4 y)2 4 x² + 16 xy + 16 y² (-4 x + 7)2 16 x²- 56 x + 49

Multiply. We can find a shortcut. (x – 2 y) This is the square of a binomial pattern. (x – y) x² = x² - xy - - 2 xy + y 2 This is a “Perfect Square Trinomial. ” xy + y 2

Multiply. Use the shortcut. (3 x - 7)2 Shortcut: x² - 2 xy + y 2 = 9 x² - 42 x + 49

Try these! (x – 7)2 x² - 14 x + 49 (3 p - 4)2 9 p² - 24 p + 16 (4 x - 6 y)2 16 x² - 48 xy + 36 y²

A mixture of all three! (2 x + 3)2 4 x² + 12 x + 9 (2 p - 4) (2 p + 4) 4 p² - 16 (2 x - y)2 4 x² - 4 xy + y²

HW • P. 593 -595 (15 -42, 63 -68)