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Multiplying a Polynomial by a Monomial

Learn how to apply the distributive property to multiply monomials and polynomials using Jonathan Gamble's horizontal method with examples, simplification techniques, and solving polynomial equations.

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Multiplying a Polynomial by a Monomial

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  1. Multiplying a Polynomial by a Monomial Jonathan Gamble

  2. Horizontal Method! The distributive property can be used to multiply a monomial and a polynomial. Example -2x2(3x2-7x+10) =-2x2(3x2)-(-2x2)(7x)+(-2x2)(10) =-6x4-(-14x3)+(-20x2) =-6x4+14x3-20x2

  3. Vertical Method 3x2-7x+10 (X) -2x2 =-6x4+14x3-20x2

  4. Simplify Expressions 4(3d2+5d)-d(d2-7d+12) =12d2+20d-d3+7d2-12d =-d3+(12d2+7d2)+(20d-12d) =-d3+19d2+8d

  5. Polynomials on both sides d(d-1)+4d=d(d-8)+22 d2-d+4d=d2-8d+22 d2+3d=d2-8d+22 3d=-8d+22 11d=22 d=2

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