Question Video: Evaluating an Expression by Using the Difference of Two Squares Mathematics • 9th Grade

By factoring or otherwise, evaluate 5 × (8.85)² − 5 × (6.85)².

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Video Transcript

By factoring or otherwise, evaluate five times 8.85 squared minus five times 6.85 squared.

In this question, we are asked to evaluate an expression. And we are told the way that we can do this is by factoring or by using any other method. We can evaluate this expression by using a calculator or by evaluating each operation separately. However, we may not always have a calculator, and evaluating each operation by hand is difficult. So instead, let’s evaluate this expression by factoring.

We can first note that both terms in the expression share a factor of five. Taking out this factor of five gives us five times 8.85 squared minus 6.85 squared. This is still a difficult expression to evaluate since we have the squares of decimals. Instead, we can note that we have a difference of two squares. And we can factor this by using the fact that 𝑎 squared minus 𝑏 squared is equal to 𝑎 minus 𝑏 times 𝑎 plus 𝑏.

Setting 𝑎 equal to 8.85 and 𝑏 equal to 6.85 and factoring using the difference of two squares gives us five times 8.85 minus 6.85 multiplied by 8.85 plus 6.85. We can now evaluate the expressions in each factor separately. First, we can calculate that 8.85 minus 6.85 is equal to two, since their decimal parts are equal. Second, we can calculate that 8.85 plus 6.85 is equal to 15.7.

Substituting these values into the expression gives us five times two times 15.7. We know that we can evaluate the product of these numbers in any order. And the easiest product to evaluate is five times two, which is equal to 10. This then gives us 10 times 15.7, which we can evaluate to give 157, which is our final answer.

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