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Which of the following expressions is equivalent to 𝑥 squared minus four minus negative two 𝑥 squared plus three?
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A) Negative 𝑥 squared minus seven.
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B) Three 𝑥 squared minus seven.
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C) Three 𝑥 squared minus one.
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Or D) negative 𝑥 squared minus one.
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Looking closely at this expression 𝑥 squared minus four minus negative two 𝑥 squared plus three, we recognize that we need to distribute this subtraction across the two values within the second parentheses.
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We need it to say plus two 𝑥 squared minus three.
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This is because subtracting negative two 𝑥 squared is the same thing as adding two 𝑥 squared and subtracting positive three is the same thing as subtracting three.
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From there, we can bring down the 𝑥 squared minus four.
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And then, we have 𝑥 squared minus four plus two 𝑥 squared minus three.
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At this point, we’ll need to combine like terms.
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We have two terms that are 𝑥 squared and two terms that are constant.
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𝑥 squared plus two 𝑥 squared equals three 𝑥 squared.
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Negative four minus three equals negative seven.
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If you start at negative four on a number line and you subtract three, you’re moving to the left.
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And you’ll get to negative seven.
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This expression is equivalent to three 𝑥 squared minus seven, which is option B.
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Option C has three 𝑥 squared minus one.
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This option has the mistake of saying negative four minus three is negative one.
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They’ve calculated negative four plus three instead of negative four minus three.
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There are also sign mistakes in option A and D.
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What’s happened here is that they’ve said 𝑥 squared minus negative two 𝑥 squared is equal to negative 𝑥 squared, which is not true.
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Instead of adding 𝑥 squared and two 𝑥 squared together, they’ve subtracted two 𝑥 squared from 𝑥 squared, which again will not produce the correct answer.
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Option B is the only option that is equivalent to the expression 𝑥 squared minus four minus negative two 𝑥 squared plus three.