1 / 9

To multiply a polynomial by a monomial , use the distributive property and the rule for multiplying exponential expre

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

alida
Download Presentation

To multiply a polynomial by a monomial , use the distributive property and the rule for multiplying exponential expre

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. (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

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

  3. 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

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

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

  6. 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

  7. 10.3 Special Cases Examples: (3x + 2)(3x – 2) (x + 1)(x – 1) = (3x)2– (2)2 = (x)2– (1)2 = 9x2– 4 = x2– 1

  8. 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

  9. 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

More Related