Multiplying Polynomials. Distributive Method Multiply each term in the first polynomial, by each term in the second polynomial. Combine like terms Example:

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Presentation transcript:

Multiplying Polynomials

Distributive Method Multiply each term in the first polynomial, by each term in the second polynomial. Combine like terms Example: 5x(6x – 10y + 3) 5x(6x) + 5x(-10y) + 5x (3) 30x ² - 50xy + 15x

(4x-5)(2x ² - 3x) 4x(2x ²) + 4x(- 3x) + -5(2x ²) + -5(- 3x) 8x³ + -12x² + -10x² + 15x 8x³ - 22x² + 15x

Practice: 1.8x (7x⁴ + 10x) 2.(4x -5)(2x + 9) 3.(2x⁴ - 5x² + 7x)(x⁵ - 7) 4.(2x – y)(3x + 5y) 1.56x ⁵ + 80x² 2.8x² + 26x – x⁹ -14x⁴ -5x⁷ + 35x² + 7x⁶ -49x 4.6x² + 7xy -5y²

Box Method Make a box and put one polynomial on the top and one polynomial on the left side Remember to bring the minus/plus signs with the appropiate terms Multiply the terms that align in the same box Combine like terms

Example: (x + 3)(2x² -10x -3) (4x -7)(3x – 10) (3xy – 7)(3x + 10y) (x² -5x + 2)(3x² + 6x – 9)

Binomial by Binomial FOIL method First Outer Inner Last (4x – 2)(3x + 10) First: 4x(3x) Outer: 4x(10) Inner: -2(3x) Last: -2(10) 12x ² -6x + 40x x ² + 34x - 20

Squaring a polynomial (3x – 5)² First separate the problem (3x-5)(3x-5) Then multiply the two polynomials! 9x² -30x + 25 Example: (2x³ - 4x)²

Shortcut =) (a + b)² = a² + 2ab + b² (a-b)² = a² - 2ab + b² Example: (2x³ - 4x)² a = 2x³b = 4x (a-b)² = a² - 2ab + b² (2x³) ² - 2(2x³ )(4x) + (4x) ² 4x⁶ - 16x⁴ + 16x² Example: (4x + 7)²

Cubing a polynomial (x -4)³ First expand (x-4)(x-4)(x-4) Multiply the first two polynomials together (x-4)(x-4) X² -8x + 16 (X² -8x + 16)(x-4) Then multiply the product and the last polynomial X³ -12X² + 48x – 64 Example: (2g²+ 4)³ 4g⁶ + 48g⁴ + 96g² + 16

(x + 3)(x – 3) X(x) + x(-3) + 3(x) + 3(-3) X² -3x + 3x – 9 X² – 9 Notice pattern?????

There is a short cut!!!! Sum & Difference of 2 terms (a +b)(a-b) = a² - b² (x +3)(x-3) a = x b = 3 (x)² - (3)² x² - 9 Practice: (3x- 8)(3x + 8) (4y + 7x)(4y -7x) (10x- 9)(9 + 10x)