1. Using the Distributive Property to Multiply Monomials and Polynomials
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Using the Distributive Property to Multiply Monomials and Polynomials

2. Concept Circles In groups of 3 or 4
Handout – in the circles you are to group terms that fit into the category of the title.
The titles of the circles are:
“Like” Terms
Exponent Rules
Algebraic Expressions

3. Concept #1-”Like” Terms In each section of the circle place “like” terms.
-6xy2
-23x2
x2y x3
5xy
11x2y2
-3x2y n3 z
34z
8z2
-z3
17x3
-4x3 7x
ab3
10xy3
-x4
2x2y
-9z

4. Concept #2-Exponent Rules In each section of the circle match an example with definition.
When bases are the same add the exponents.
When bases are the same subtract the exponents.
When there is a power to a power, multiply the exponents.
x5 ÷ x2 = x3
(3a4)2 = 9a8
y2 x y4 = y6

5. Concept #3-Algebraic Expressions Match a term with an example and the number of terms.
Terms: Binominal Monomial Trinomial
Number of Terms:
1 term
2 terms
3 terms
Examples:
x2 - 3x + 4 2x
5x3 + 6

6. Review Adding and Subtracting Polynomials Examples
Collecting “like” terms. Two terms are alike if they have the same variable and the same exponent.
Examples
Simplify each expression.
2n+4w+5n+w+9n b) (4x+7y+9)-(6x-8y+11)
= 16n+5w = -2x+15y-2

7. More Review Exponent Rules Examples
Multiplying powers with the same base, keep the base the same and add the exponents.
Dividing powers with the same base, keep the base the same and subtract the exponents.
Power to an exponent, keep the base the same and multiply the exponents.
Examples
Simplify each of the following.
22x28 b) 49÷46 c) (x3)6
= = = x18
= = 64

8. Monomial x Monomial
Multiply the coefficients together and then multiply powers with the same base by applying the exponent rules.
Examples
Simplify each of the following.
(4pq)(-6p2q3) b) (xy2)2(x3y)4
= -24p3q4 = (x2y4)(x12y4)
= x14y8

9. Monomial x Polynomial Examples
To multiply a multi-termed polynomial by a monomial, simply multiply each term in the polynomial by the monomial using the distributive property.
Examples
Multiply 3(3x3-2x2+8x-7).
= 9x3-6x2+24x-21
Simplify 4x7+9x4-7+2x2(8x5-5x2).
= 4x7+9x4-7+16x7-10x4
= 20x7-x4-7
Divide (14x9+49x6-42x4)÷7x3.
= 2x6+7x3-6x

10. More Monomial x Polynomial
Students TRY: Multiply: 1.) 4x(5x3-2x2+x-6) 2.) 2xy(4x3y2-6xy) Divide: 1.) (16a6+32a4-8a3) ÷ 4a2 2.) (35z7-20z3-15z) ÷5z Simplify: 1.) 9x4-12xy+3x(x3+2y-4)

11. Homework
Worksheet

12. Write 2–3 things that you have learned today.
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This is to be done privately, no sharing!
Plus “+” Δ
Write 2–3 things that you have learned today.
Write 2-3 things that you would add/change about today - or something you had difficultly with.