Algebra I : Semester II : Polynomials

Sections:

Introduction  |   Section 1  |   Section 2  |   Section 3  |  Section 4  |  Section 5  |  Section 6

Section Three

Part 1  |  Part 2  |  Part 3  |  Part 4  |  Part 5

Algebra 1: Section 3: Polynomials Multiplying Monomials Review In the first semester, you learned how to multiply monomials. Here is a quick review, as the rules listed are important to understand the rest of the lesson.   Click here for a presentation on Multiplying Monomials   Multiplying Monomials Rule Symbols Examples Product of Powers To multiply two powers that have the same base, add the exponents. am ∙ an = am+n a4 ∙ a9 = a13 Power of a Power To find the power of a power, multiply the exponents. (am)n = am∙n (a3)4 = a12 Power of a Product To find the power of a product, find the power of each factor and multiply. (ab)n = anbn (2a3)4 = 16a12   Another Way to Look at It Group coefficients and common bases Multiplying — add exponents Power to a power — multiply exponents Product to a power — take each to the power Example 1: Finding a Product Simplify each expression. (3z5)(-z8) = (3 · -1)(z5 · z8) Group     (–z8 = -1z8 by the multiplicative identity) = -3z13 Multiply constants and add exponents (-4xy3)(-2x5y5) = (-4 · -2)(x · x5)(y3 · y5) Group = 8x6y8 Multiply and add exponents (5x-1)(3x3y)(-4yz) = (5 · 3 · -4)(x-1 · x3)(y · y)(z) Group = -60x-1+3y1+1z  Multiply constants and add exponents = -60x2y2z  Simplify Example 2: Power of Power Simplify (-2x5y-1)4 . = (-2)4 (x5)4 (y-1)4   Product to a power – take each to the power = 16 x5∙4 y-1∙4        Power to a power – multiply exponents = 16x20y-4            Simplify = 16x20/ y4          Simplify (you cannot have negative exponents in your final answer)   Example 3:  Simplify Expressions Simplify . Use order of operations and begin with the inside parenthesis. product to a power – take each to the power power to a power – multiply exponents group coefficients and common bases multiplying – add exponents Quick Practice Simplify each of the following. (-2mn3)(7mn2) = -14m2n5 x(-x5)(x2) = -x8 (5ab4)3 = 125a3b12 (-3p3q2)4 = 81p12q8 (4ac)2(-3a2c3)3 = (16a2c2)(-27a6c9) = -432a8c11 (9a3)(-2a2b2)(4ab4) = -72a6b6 Now go on to the next part

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