Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 4 Polynomials

1-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Special Products Products of Two Binomials Multiplying Sums and Differences of Two Terms Squaring Binomials Multiplications of Various Types 4.6

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. The FOIL Method To multiply two binomials, A + B and C + D, multiply the First terms AC, the Outer terms AD, the Inner terms BC, and then the Last terms BD. Then combine like terms, if possible. (A + B)(C + D) = AC + AD + BC + BD Multiply First terms: AC. Multiply Outer terms: AD. Multiply Inner terms: BC. Multiply Last terms: BD. ↓ FOIL (A + B)(C + D) O I F L

1-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply: (x + 4)(x 2 + 3) Solution The terms are rearranged in descending order for the final answer.

1-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply. a) (x + 8)(x + 5)b) (y + 4) (y  3) c) (5t 3 + 4t)(2t 2  1)d) (4  3x)(8  5x 3 ) Solution

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. The Product of a Sum and Difference The product of the sum and difference of the same two terms is the square of the first term minus the square of the second term. (A + B)(A – B) = A 2 – B 2. This is called a difference of squares.

1-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply. a) (x + 8)(x  8) b) (6 + 5w) (6  5w) c) (4t 3  3)(4t 3 + 3) Solution

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. The Square of a Binomial The square of a binomial is the square of the first term, plus twice the product of the two terms, plus the square of the last term. (A + B) 2 = A 2 + 2AB + B 2 ; (A – B) 2 = A 2 – 2AB + B 2 ; These are called perfect-square trinomials.* *Another name for these is trinomial squares.

1-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply. a) (x + 8) 2 b) (y  7) 2 c) (4x  3x 5 ) 2 Solution

1-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Multiply: a) (x + 5)(x  5)b) (w  7)(w + 4) c) (x + 9)(x + 9)d) 3x 2 (4x 2 + x  2) e) (p + 2)(p 2 + 3p  2)f) (2x + 1) 2 Solution