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How Do You Multiply a Monomial by a Polynomial?

Find the product of (3a)(2a2+4ab2-5ab)

Summary

  1. Product means multiplication
  2. 3a is a monomial
  3. 2a2+4ab2-5ab is a polynomial
  4. Distribute the 3a by multiplying by each term in the polynomial
  5. 3a•2a2=6a3
  6. 3a•4ab2=12a2b2
  7. 3a•-5a2b=-15a2b
  8. Add the terms together to get the answer

Notes

    1. We need to distribute the 3a through the polynomial
    1. So we need to multiply 3a by each monomial in the polynomial
    1. 3a and 2a2 are both monomials
    2. Multiply the coefficients, 3 times 2, to get 6
    3. Multiply the variables, a times a2, to get a3
    1. 3a and 4ab2 are both monomials
    2. Multiply the coefficients, 3 times 4, to get 12
    3. Multiply the 'a' variables, a times a, to get a2
    4. 3a doesn't have a b variable, so we multiply the b2 by 1 and get b2 in our product
    1. 3a and -5ab are both monomials
    2. Multiply the coefficients, 3 times -5, to get -15
    3. Multiply the 'a' variables, a times a2, to get a3
    4. 3a doesn't have a b variable, so we multiply the b by 1 and get b in our product
    1. Now we just combine the terms to get our answer
    1. 6a3 and 12a2b2 are terms in our solution
    1. When we multiplied 3a times -5ab, we got a negative coefficient
    2. So we can just use that subtraction sign, since adding a negative is the same as subtracting