1 / 9

7.6 Factoring Differences of Squares

7.6 Factoring Differences of Squares. CORD Math Mrs. Spitz Fall 2006. Product of sum and difference.

hazela
Download Presentation

7.6 Factoring Differences of Squares

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. 7.6 Factoring Differences of Squares CORD Math Mrs. Spitz Fall 2006

  2. Product of sum and difference • The product of the sum and difference of two expressions is called “the difference of squares.” The process for finding this product can be reversed in order to factor the difference of squares. Factoring the difference of squares can be modeled geometrically.

  3. Difference of Squares a2 – b2 = (a – b)(a + b) = (a + b)(a – b)

  4. Ex. 1: Factor a2 - 64 • You can use this rule to factor trinomials that can be written in the form a2 – b2. a2 – 64 = (a)2 – (8)2 = (a – 8)(a + 8)

  5. Ex. 2: Factor 9x2 – 100y2 • You can use this rule to factor trinomials that can be written in the form a2 – b2. 9x2 – 100y2 = (3x)2 – (10y)2 = (3x – 10y)(3x + 10y)

  6. Ex. 3: Factor • You can use this rule to factor trinomials that can be written in the form a2 – b2.

  7. Ex. 4: Factor 12x3 – 27xy2 • Sometimes the terms of a binomial have common factors. If so, the GCF should always be factored out first. Occasionally, the difference of squares needs to be applied more than once or along with grouping in order to completely factor a polynomial. 12x3 – 27xy2 = 3x(4x2 – 9y2) = 3x(2x – 3y)(2x + 3y)

  8. Ex. 5: Factor 162m4 – 32n8 162m4 – 32n8 = 2(81m4 – 16n8) = 2(9m2 – 4n4)(9m2 + 4n4) = 2(3m – 2n2)(3m + 2n2)(9m2 + 4n4) 9m2 + 4n4 cannot be factored because it is not a difference of squares.

  9. The measure of a rectangular solid is 5x3 – 20x + 2x2 – 8. Find the measures of the dimensions of a solid if each one can be written as a binomial with integral coefficients. 5x3 – 20x + 2x2 – 8= (5x3 – 20x) + (2x2 -8) = 5x(x2 – 4) + 2(x2 - 4) = (5x+ 2)(x2 - 4) = (5x + 2)(x – 2)(x + 2) The measures of the dimensions are (5x + 2), (x – 2), and (x + 2).

More Related