Multiplying a Polynomial and a Monomial Date_____ Period____ Find each product. 1) 8 x(6x + 6) 2) 7n(6n + 3) 3) 3r(7r − 8) 4) 8(8k − 8) 5) 10 a(a − 10 b) 6) 2(9x − 2y) 7) 7x(6x + 4y) 8) 4a(8a − 8b) 9) 3n(n2 − 6n + 5) 10) 2k3(2k2 + 5k − 4) 11 ...

A monomial is an expression that is a number, variable or product of a number and variables. Examples of monomials: –3, 4x, 5xy, y2 A polynomial is a monomial or the sum or difference of monomials. Examples of polynomials: 2x + 4, –x4 + 4x3 – 5x2, 400 To multiply a monomial by a polynomial, use the distributive property. Distributive Property

Multiplying Polynomials by Monomials (The Distributive Property) 19. An open-top box will be created by removing square corners from a rectangular piece of cardboard and then folding up the resulting flaps. The length of the original piece of cardboard is 80 cm. The width of the box will be three times the side length of the removed squares.

Multiplying a Polynomial and a Monomial 1) T2+3 T 2) −8 T+16 2 3) 24 T+2 T 4) 2− T 2+3 T 5) 9 T2−6 T 6) 15 T−30 U 7) 56 T2−32 T 8) 227 T+6 T U 9) 26 T+12 T U 2 10) 18 T2+36 T U T 11) 36 T2+108 T 18 12) 22 T2−121 T U 24 13) 12 T2−12 T U 6 14) 6 T2−12 T U+6 T 4

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Multiplying Monomials When multiplying two monomial terms, such as (8 3)(3 4), mentally reorder the factors to get (8∙3)( 3∙ 4). Then multiply using the rules for exponents: 24 7. The Distributive Property: ( + )= When multiplying a monomial by another polynomial, use …

7.3 Divide a Polynomial by a Monomial Using Symbols 7.3 Divide a Polynomial by a Monomial Using a Model 7.2 Multiply a Polynomial by a Monomial Using Symbols 7.2 Multiply a Polynomial by a Monomial Using Algebra Tiles 7.2 Multiply a Polynomial by a Monomial Using an Area Model Multiplying and Dividing Polynomials by Monomials Using the Foldable

D. Multiplying Polynomials By Monomials A monomial is a one-term polynomial. Use the distributive property. Find E. Multiplying Binomials A binomial is a two-term polynomial. Method 1: Distributive Property If the problem is to expand, we distribute the to the two terms of the second binomial: Now use the distributive property again to get

Polynomials - Multiplying Polynomials Objective: Multiply polynomials. Multiplying polynomials can take several different forms based on what we are multiplying. We will first look at multiplying monomials, then monomials by polynomials and finish with polynomials by polynomials. Multiplying monomials is done by multiplying the numbers or ...

Multiplying a Polynomial and a Monomial Date_____ Period____ Find each product. 1) 8x(6x + 6) 2) 7n(6n + 3) 3) 3r(7r − 8) 4) 8(8k − 8) 5) 10a(a − 10b) 6) 2(9x − 2y) 7) 7x(6x + 4y) 8) 4a(8a − 8b) 9) 3n(n2 − 6n + 5) 10) 2k3(2k2 + 5k − 4) 11) 8r2(4r2 − 5r + 7) 12) 3(3v2 + 8v − 5)