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Rewrite an equivalent expression for the sum of 75+30

in 2 different ways using the distributive property and a common factor.

1 answer

To use the distributive property and a common factor for the sum of \(75 + 30\), we can first identify a common factor. The common factor for both 75 and 30 is 15.

  1. Factoring out the common factor: \[ 75 + 30 = 15 \times 5 + 15 \times 2 = 15(5 + 2) \]

  2. Using the distributive property with a different grouping: \[ 75 + 30 = 70 + 5 + 30 = 70 + (5 + 30) = 70 + 35 = 70 + 15 \times 2 = 15 \times 5 + 15 \times 2 \]

So, the two equivalent expressions using the distributive property and a common factor are:

  1. \(15(5 + 2)\)
  2. \(15(5) + 15(2)\)