# Algebra - Polynomials Multiplication

 Multiplying monomials. =  = Multiplying monomials. =  =   Multiplying monomials. =  = Multiplying a Monomial by a Polynomial. Multiplying a Monomial by a Polynomial. Multiplying Binomials. *Each term in the first polynomial must be multiplied by each term in the second. + Multiplying Binomials. *Each term in the first polynomial must be multiplied by each term in the second. Multiplying a binomial by a trinomial. *Each term in the first polynomial must be multiplied by each term in the second. x(5x2)+x(-2x)+x(-6)+4(5x2)+4(-2x)+4(-6) 5x3-2x2-6x+20x2-8x-24 Formula for "Special Case Products" The product of congugates results in a ______ of ________. The square of a binomial results in a _______ _______ trinomial. differencesquaresperfectsquare Special Case Formula #1: a2-ab + ab -b2 (difference of squares) Special Case Formula #2: (a+b)(a+b)a2+ab+ab+b2 (perfect square trinomial) The product of conjugates results in a ______ of _______. differencesquares The square of a binomial results in a _______ _______ trinomial. perfectsquare Find a polynomial that represents the volume of the cube: V= (x+4)(x+4)(x+4) Step 1: Multiplying from left to right, you notice that you're squaring a binomial. So, you'll get a perfect square trinomial. Step 2: Rewrite the equation:   Step 3: Multiply each term in first parentheses by each term in the 2nd. x2*x+x2*4+8x*x+8x*4+16*x+16*4 x3 + 4x2 + 8x2 + 32x + 16x + 64 Step 4: Combine like terms: V = Multiplying Conjugates. Once you recognize the conjugate, you know you will end up with a difference in squares, so you don't have to multiply the "long way". Multiplying Conjugates. Once you recognize the conjugate, you know you will end up with a difference in squares, so you don't have to multiply the "long way". Squaring Binomials. We know that the result will be a perfect square trinomial. So, you don't have to multiply (a+b)(a+b) the long way.  (2x)2 +2(2x)(5) + (5)2 SAME AS: Squaring Binomials. We know that the result will be a perfect square trinomial. So, you don't have to multiply (a+b)(a-b) the long way. Just remember to put the negative sign in front of the middle term. (3y2)2 - 2(3y2)(7w) + (7w)2 Authorrandycapped ID267638 Card SetAlgebra - Polynomials Multiplication DescriptionMultiplying Polynomials Updated2014-03-24T05:24:19Z Show Answers