Factoring the Difference of Two Squares | Lecture Note - Edubirdie

University:
Campbell University
Course:
MATH 111 | College Algebra
Academic year:

2022
Views:

265

Pages:

1
Author:

Cory Singh

Factoring the Difference of Two Squares Multiplying a binomial by its conjugate yields another special product called the Difference of Two Squares. (a + b)(a - b) = a2 + ab - ab - b2 = a2 - b2 Recall: (This is the only time the Outer & Inner products of FOIL cancel each other out!) Our job is to recognize the difference of squares and factor it. Example: 4x2 - 9y2 Both terms are perfect squares (coefficient and variable) with opposite signs. Its factors are the conjugate binomials: (2x + 3y)(2x - 3y) Using “self-talk” works well: (sq rt of 1st term “+” sq rt of 2nd term)(sq rt of 1st term “-” sq rt of 2nd term) Writing (or “picturing”) 4x2 - 9y2 as (2x)2 - (3y)2 helps too. 4x2 - 9y2 = (2x)2 - (3y)2 = (2x + 3y)(2x - 3y) REMEMBER: The sum of squares (4x2 + 9y2) is NOT FACTORABLE! Can you factor 9x2 - 12xy + 4y2 - 4

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