Question Video: Evaluating Numerical Expressions with Integer Exponents Using the Distributive Property | Nagwa Question Video: Evaluating Numerical Expressions with Integer Exponents Using the Distributive Property | Nagwa

Question Video: Evaluating Numerical Expressions with Integer Exponents Using the Distributive Property

Using the distributive property, calculate 59² + 59 × (−49).

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Video Transcript

Using the distributive property, calculate 59 squared plus 59 times negative 49.

When we’re using the distributive property, we can remove common factors from two terms. At first, it might not seem like these two terms share any common factors. Remember, in an expression like this, these would be the two terms. We’re combining 59 squared and 59 times 49. But we could rewrite this 59 squared as 59 times 59, which is being added to 59 times negative 49. And that’s when we recognize that both of these terms share a factor of 59. If we undistribute a factor of 59, we’ll take it out and then we’ll open the parentheses, as we’ll be multiplying 59 by what is remaining in the two terms.

If we remove a factor of 59 from the first term, 59 is remaining. This is because 59 squared is equal to 59 times 59. And if we remove a factor of 59 from our second term, we’ll be left with negative 49. But once we do this, we know that we’re able to add inside the parentheses. And that means we can add 59 and negative 49, which is equal to 10. And we need to multiply that 10 by a factor of 59, which gives us 590.

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