The third method is the Box Method. This （第三个方法是框的方法。）.pdf

MULTIPLYING POLYNOMIALS METHOD 1: Use the Distributive Property 3x(x +5) = 3x∙x + 3x ∙5 = 3x2 + 15x Multiplying Binomials (3x + 5)(2x – 1) = (3x + 5)(2x) + (3x + 5)(-1) = (3x)(2x) + (5)(2x) + (3x)(-1) + 5(-1) = 6x2 + 10x + -3x + -5 Now combine like terms: =6x2 + 7x - 5 Multiplying a binomial and a trinomial (2x + 1)(x2 – 3x +5) 2 =(2x + 1)(x ) + (2x+1)(-3x) + (2x+1)(5) 3 2 2 = 2x + x + (-6x ) + (-3x) + 10x + 5 = 2x3 -5x2 + 7x + 5 Multiplying Larger Polynomials Using the Distributive Property The Vertical Method of multiplication is sometimes more efficient. 2 (3x + 2)(x - x+4) Just as you would in multiplying whole x 2 x 4 numbers, put the larger polynomial (the one with more terms) on top and the smaller  3x 2 polynomial on the bottom. Multiply every term in the larger polynomial 2x 2 2x 8 by 2 (the last term in the other polynomial). 3 2 Then on the next line multiply every term in 3x 3x 12x the larger polynomial by the next term in the smaller polynomial (3x). Make sure to line up 3 2 3x x 10x 8 like terms. Multiply : x 2 2x 7x 2 x 2 2x 7  x 2 METHOD 2: FOIL (First, Outer, Inner, Last) - This only works for multilying binomials (polynomials with only 2 terms) (3x + 5)(2x – 1) The First terms in each of these binomials are 3x and 2x. The Outer terms are the ones on the “outsides” of the binomials, 3x and -1. The Inner terms are the ones in the middle, 5 and 2x. The Last terms are the second terms of each binomial, 5 and -1. FOIL = (3x)(2x) + (3x)(-1) + (5)(2x) + 5(-1) = 6x2 + -3x + 10x + -5 Now combine like terms: =6x2 + 7x - 5