(B12) Multiplying Polynomials

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Presentation transcript:

(B12) Multiplying Polynomials To multiply a polynomial by a monomial, use the distributive property and the rule for multiplying exponential expressions. Examples:. Multiply: 2x(3x2 + 2x – 1). = 2x(3x2 ) + 2x(2x) + 2x(–1) = 6x3 + 4x2 – 2x

Multiplying Polynomials Multiply: – 3x2y(5x2 – 2xy + 7y2). = – 3x2y(5x2 ) – 3x2y(– 2xy) – 3x2y(7y2) = – 15x4y + 6x3y2 – 21x2y3

Multiplying Polynomials To multiply two polynomials, apply the distributive property. Example: Multiply: (x – 1)(2x2 + 7x + 3). = (x – 1)(2x2) + (x – 1)(7x) + (x – 1)(3) = 2x3 – 2x2 + 7x2 – 7x + 3x – 3 = 2x3 + 5x2 – 4x – 3

Multiplying Polynomials Examples: Multiply: (2x + 1)(7x – 5). = 2x(7x) + 2x(–5) + (1)(7x) + (1)(– 5) = 14x2 – 10x + 7x – 5 = 14x2 – 3x – 5

Multiplying Polynomials Multiply: (5x – 3y)(7x + 6y). = 5x(7x) + 5x(6y) + (– 3y)(7x) + (– 3y)(6y) = 35x2 + 30xy – 21yx – 18y2 = 35x2 + 9xy – 18y2

10.3 Special Cases The multiply the sum and difference of two terms, use this pattern: (a + b)(a – b) = a2 – ab + ab – b2 = a2 – b2 square of the second term square of the first term

10.3 Special Cases Examples: (3x + 2)(3x – 2) (x + 1)(x – 1)

Special Case To square a binomial, use this pattern: (a + b)2 = (a + b)(a + b) = a2 + ab + ab + b2 = a2 + 2ab + b2 square of the first term twice the product of the two terms square of the last term

Special Case Examples: Multiply: (2x – 2)2 . = (2x)2 + 2(2x)(– 2) + (– 2)2 = 4x2 – 8x + 4 Multiply: (x + 3y)2 . = (x)2 + 2(x)(3y) + (3y)2 = x2 + 6xy + 9y2