4 Multiplying Polynomials To multiply two monomials, multiply the coefficients and use the product rule of exponents.Example: (7x3)(6x5) = 7 · x36 · 6 · x5 = 42x8To multiply a polynomial by a monomial, use the distributive property: a(b + c) = ab + acExample: Multiply 3x(2x2 + 4)3x(2x2 + 4) = (3x)(2x2) + (3x)(4) = 6x3 + 12x
5 Multiplying Polynomials To multiply two binomials, use the distributive property so every term in one polynomial is multiplied by every term in the other polynomial.Example:a.) (x + 3)(x + 4) = (x + 3)(x) + (x + 3)(4) = x2 + 3x + 4x+ 12 = x2 + 7x + 12A common method used to multiply two binomials is the FOIL method.
6 The FOIL Method F O I L Consider (a + b)(c + d): Stands for the first – multiply the first terms together.(a + b) (c + d): product acStands for the outer – multiply the outer terms together.(a + b) (c + d): product adOStands for the inner – multiply the inner terms together.(a + b) (c + d): product bcIStands for the last – multiply the last terms together.L(a + b) (c + d): product bdThe product of the two binomials is the sum of these four products: (a + b)(c + d) = ac + ad + bc + bd
7 The FOIL Method Using the FOIL method, multiply (2x - 3)(x + 4) . + (-3)(4)L= (2x)(x)(2x - 3) (x + 4)F+ (-3)(x)IO+ (2x)(4)= 2x x x= 2x 2 + 5x - 12
8 Formulas for Special Products Product of the Sum and Difference of the Same Two Terms(a + b)(a – b) = a2 – b2The expression on the right side of the equals sign is called the difference of two squares.Example:a.) (x + 5) (x – ) = x2 - 25
9 Formulas for Special Products Square of Binomials(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2To square a binomial, add the square of the first term, twice the product of the terms and the square of the second term.Example:a.) (x + 5)2 = (x)2 + 2(x)(5) + (5)2 = x2 + 10x + 25