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10.3

Multiplying Polynomials. 10.3. Multiplying Monomials. To multiply two monomials use the associative and commutative properties and regroup. Remember that to multiply exponential expressions with a common base, add exponents. Use the commutative and associative properties.

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10.3

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  1. Multiplying Polynomials 10.3

  2. Multiplying Monomials To multiply two monomials use the associative and commutative properties and regroup. Remember that to multiply exponential expressions with a common base, add exponents. Use the commutative and associative properties. Use the product rule for exponents. Simplify.

  3. Multiplying Monomials by Polynomials To multiply a monomial and any polynomial, we use the distributive property and properties of exponents. a(b+c) =a∙b+a∙c

  4. Multiplying Monomials by Polynomials Apply the distributive property. 3x∙5x2 + 3x∙4 = 15x3 + 12x 3x(5x2 + 4) = 4z(2z2 + 5z– 6) = 4z•2z2 + 4z•5z + 4z•(– 6) = 8z3 + 20z2– 24z

  5. Multiplying Two Polynomials To multiply two binomials, we use a version of the distributive property. (b+c)a=b∙a+c∙a (x+2)(x+ 3) =x(x+ 3) +2(x+ 3) =x∙x+x∙3 + 2∙x+ 2∙3 =x2+3x+ 2x+ 6 =x2+5x+ 6

  6. Multiplying Two Polynomials To Multiply Two Polynomials Multiply each term of the first polynomial by each term of the second polynomial and then combine like terms.

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