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How Do You Find the Volume of a Box Whose Sides are Monomials?

Find the volume of a rectangular box whose sides have the following lengths:
Side 1 = 3a2
Side 2 = 2a2b
Side 3 = 2/3 • a2b3
Write your answer as a polynomial in simplest form.

Summary

  1. 'a' and 'b' are variables
  2. Notice that each side is a monomial
  3. Use the associative property of multiplication to group terms together
  4. When multiplying variables we can just add the exponents
  5. a2•a2•a2=a2+2+2=a6
  6. b•b3=b1+3=b4

Notes

    1. 'a' and 'b' are variables
    2. The length is side 1, 3a2
    3. The width is side 2, 2a2b
    4. The height is side 3, 2/3 • a2b3
    1. The volume of the box is (side 1)•(side 2)•(side 3)
    1. 'a' and 'b' are variables
    2. Notice that the sides are monomials
    1. The constants were 3, 2 and 2/3
    1. 'a' is a variable
    2. Our 'a' terms were a2, a2 and a2
    1. 'b' is a variable
    2. Our 'b' terms were b and b3
    1. First let's multiply the constants together
    2. The constants are 3, 2 and 2/3
    1. We can just add the exponents together to find the product
    2. 'a' is a variable
    3. a2•a2•a2=a2+2+2=a6
    1. We can just add the exponents together to find the product
    2. 'b' is a variable
    3. 'b' is the same as b1
    4. b•b3=b1+3=b4
    1. 'a' and 'b' are variables