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Video: Using the Distributive Property of Multiplication to Expand Expressions Containing Brackets

Bethani Gasparine

Bruce had 10 dollars in his savings account and then he deposited $11. Seven months later, his balance had doubled. Which of the following is equivalent to his new balance of 2(𝑏 + 11) dollars.

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Video Transcript

Bruce has 𝑏 dollars in his savings account, and then he deposited eleven dollars. Seven months later, his balance has doubled. Write an equivalent expression to his new balance of two times 𝑏 plus eleven dollars.

In order to write an equivalent expression, we can simplify what we have. Essentially, when the two is outside of these parentheses, we’re multiplying; it’s called the distributive property. So we will take two times 𝑏 and add it to two times eleven.

To help visualize, we can use arrows. So the two multiplies to the 𝑏 and the two also multiplies to the eleven, and we add those together, so two times 𝑏 is two 𝑏 and two times eleven is twenty-two. Therefore, the equivalent expression to his new balance would be two 𝑏 plus twenty-two.