Using the Distributive Property to Multiply Monomials and Polynomials

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Presentation transcript:

Using the Distributive Property to Multiply Monomials and Polynomials Expanding Using the Distributive Property to Multiply Monomials and Polynomials

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

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

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

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

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

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 = 210 = 43 = x18 = 1024 = 64

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

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

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)

Homework Worksheet

Write 2–3 things that you have learned today. Expanding 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.