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 Polynomials   Click here for a presentation on Multiplying Polynomials Now let’s sum up what we just learned.   To Multiply Polynomials Distribute each term in the first polynomial times each term in the second. Multiply. Add like terms. Example 1: Multiplying Binomials Multiply (3x + 1)(x – 5). = 3x(x) + 3x(-5) + 1(x) + 1(-5)      Distribute 3x and distribute 1 = 3x2 – 15x + x – 5                    Multiply = 3x2 – 14x – 5                          Add like terms Example 2: Two Variables Multiply (a + b) (2a + 3b) = a(2a) + a(3b) + b(2a) + b(3b)        Distribute a and b = 2a2 + 3ab + 2ab + 3b2                 Multiply = 2a2 + 5ab + 3b2                          Add like terms  When you have two variables, list alphabetically. Example 3: Multiplying with Trinomials Multiply the following. (2x – 1) (2x2 + 7x – 2) = 2x(2x2) + 2x(7x)  + 2x(-2) + (-1)(2x2) + (-1)(7x) + (-1)(-2) Distribute 2x and -1 = 4x3 + 14x2 – 4x – 2x2 – 7x + 2 Multiply = 4x3 + (14x2 – 2x2) + (-4x + -7x) + 2 Group like terms = 4x3 + 12x2 – 11x + 2 Add like terms Example 4: Finding Areas Find the area of each of the following. Rectangle A = LW A = LW A = (x + 3)(2x – 4) A = 2x2 – 4x + 6x – 12 A = 2x2 + 2x – 12 Triangle A = 1/2bh or A = 0.5bh A = ½ b h A = ½ (2x – 4)(x + 8) A = (x – 2)(x + 8) A = x2 + 8x – 2x – 16 A = x2 + 6x – 16 Trapezoid A = 1/2(b1 + b2)h or A = 0.5(b1 + b2)h A = ½ (b1 + b2)(h) A = ½ (2x + 2 + 4x + 2)(x + 2) A = ½ (6x + 4)(x + 2) A = (3x + 2)(x + 2) A = 3x2 + 8x + 4 Circle A = πr2, where π = 3.14 A = π r 2 A = 3.14(2x + 2)2 A = 3.14(2x + 2)(2x + 2) In this case it would be simpler to multiply the binomials first. A = 3.14(4x2 + 4x + 4x + 4) A = 3.14(4x2 + 8x + 4) A = 12.56x2 + 25.12x + 12.56 Now go on to the next part

© 2006 Aventa Learning. All rights reserved.