# Video: US-SAT05S4-Q08-832164574968

Which of the following expressions is equivalent to (π₯Β² β 4) β (β2π₯Β² + 3)? [A] βπ₯Β² β 7 [B] 3π₯Β² β 7 [C] 3π₯Β² β 1 [D] βπ₯Β² β 1.

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### Video Transcript

Which of the following expressions is equivalent to π₯ squared minus four minus negative two π₯ squared plus three? A) Negative π₯ squared minus seven. B) Three π₯ squared minus seven. C) Three π₯ squared minus one. Or D) negative π₯ squared minus one.

Looking closely at this expression π₯ squared minus four minus negative two π₯ squared plus three, we recognize that we need to distribute this subtraction across the two values within the second parentheses. We need it to say plus two π₯ squared minus three. This is because subtracting negative two π₯ squared is the same thing as adding two π₯ squared and subtracting positive three is the same thing as subtracting three.

From there, we can bring down the π₯ squared minus four. And then, we have π₯ squared minus four plus two π₯ squared minus three. At this point, weβll need to combine like terms. We have two terms that are π₯ squared and two terms that are constant. π₯ squared plus two π₯ squared equals three π₯ squared. Negative four minus three equals negative seven. If you start at negative four on a number line and you subtract three, youβre moving to the left. And youβll get to negative seven.

This expression is equivalent to three π₯ squared minus seven, which is option B. Option C has three π₯ squared minus one. This option has the mistake of saying negative four minus three is negative one. Theyβve calculated negative four plus three instead of negative four minus three. There are also sign mistakes in option A and D.

Whatβs happened here is that theyβve said π₯ squared minus negative two π₯ squared is equal to negative π₯ squared, which is not true. Instead of adding π₯ squared and two π₯ squared together, theyβve subtracted two π₯ squared from π₯ squared, which again will not produce the correct answer. Option B is the only option that is equivalent to the expression π₯ squared minus four minus negative two π₯ squared plus three.