Writing Products as Sums and Sums as Products – Practice Problems

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To express a product as a sum, apply the distributive property of multiplication over addition. And the other way around, to express a sum as a product, apply factoring. The ability to rewrite an expression in a different form allows flexibility and opens the mind to various possibilities in solving a mathematical problem. Learn how to express products as sums and sums as products by helping superhero En Fuego prepare a training regimen that would allow her to match the skills of her arch-rival superhero Ice Queen, the reigning champion, in a duel for this year’s upcoming Superhero supremacy showdown. Common Core Reference: CCSS.MATH.CONTENT.7.EE.A.1

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Exercises in this Practice Problem
Explain how to express the product $4(32x+2)$ as a sum.
Determine how the different factors alter the expression $16x+1$.
Explain how to express the sum $120x+16$ as a product.
Write each sum as a product.
State how to express the product $4(16x+1)$ as a sum.
Represent products as sums and vice versa.