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Polynomial Multiplication with Monomials: Distributive Property & Exponent Rules

Learn how to multiply a polynomial by a monomial using the distributive property and exponent rules. Follow steps to combine like terms and simplify expressions in descending order. Solve equations with polynomial expressions.

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Polynomial Multiplication with Monomials: Distributive Property & Exponent Rules

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  1. Chapter 8 sec.6 How do I multiply a polynomial by a monomial

  2. Use the DISTRIBUTIVE PROPERTY and EXPONENT RULES Steps: 1. multiply the numbers 2. keep the base(variable) 3. add the exponents

  3. EX: 1. -2x2 (3x2 – 7x +10) = -6x4 + 14x3 – 20x2 2. 5y(-2y2 – 7y) = -10y3 – 35y2 3. -2b2( 3b2 – 4b +9) = -6b4 + 8b3 – 18b2

  4. continued… -2xy ( -3x2y – 4y + 2x2 ) = 6x3y2 + 8xy2 – 4x3y 4(3d2 + 5d) –d(d2 -7d +12) distribute 12d2 +20d –d3 + 7d2 – 12d combine like terms

  5. Descending order: Put terms in order according to the X exponents.

  6. Solve Equations with polynomial expressions Same steps as solving any other equations: 1. distribute 2. Combine like terms 3. Collect like terms (get on the same side) 4. add/subtract any constants 5. Multiply/divide to isolate.

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