Unit 2 - Objective 2 - Multiplying Polynomials

You may need to review Unit 1 - Objective 4 - Rules of Exponents again. Remember am · an = am + n.

Examples:
 1 (3x3) (- 7bx4) = - 21bx3 + 4 = - 21bx7 2 (- 5xy2z3) (3x2y2) = -15x1 + 2y2 + 2z3 = -15x3y4z3

If a mononomial is raised to a power, first raise it to the indicated power before multiplying the rest of the problem.

Examples:
 1. 5 (2x2y3)2 = 5 (22 (x2)2 (y3)2) = 5 (4x4y6) = 20x4y6 2. 2a3 (-ab4)2 (4a2b) = 2a3 ((-a)2 (b4)2) (4a2b) = 2a3 (a2b8) (4a2b) = (2) (4) a3 + 2 + 2 b8 + 1 = 8a7b9

To find the product of a mononomial and a polynomial use the distributive law.

Examples:

 1. 4x2y (3xy2 + 2x3y) = (4x2y) (3xy2) + (4x2y) (2x3y) = 12x2 + 1y1 + 2 + 8x2 + 3y1 + 1 = 12x3y3 + 8x5y2 2. - 7ab2 (2ax3 - 5abx + 3b3) = (-7ab2) (2ax3) + (- 7ab2) (- 5abx) + (-7ab2) (3b3) = -14a1 + 1b2x3 +35a1 + 1b2 + 1x - 21ab2 + 3 = -14a2b2x3 + 35a2b3x - 21ab5

To multiply polynomials use the distributive law and the laws of exponents. Remember the FOIL Method when multiplying two binomials which is Multiply First terms, Outside terms, Inside terms, Last terms.

 Examples: NOTE: (The second line of #2 - I forgot the term +(-3c)(a2))