Which of the following expressions is equivalent to 𝑥 squared minus four minus negative two 𝑥 squared plus three? A) Negative 𝑥 squared minus seven. B) Three 𝑥 squared minus seven. C) Three 𝑥 squared minus one. Or D) negative 𝑥 squared minus one.
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. We need it to say plus two 𝑥 squared minus three. 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.
From there, we can bring down the 𝑥 squared minus four. And then, we have 𝑥 squared minus four plus two 𝑥 squared minus three. At this point, we’ll need to combine like terms. We have two terms that are 𝑥 squared and two terms that are constant. 𝑥 squared plus two 𝑥 squared equals three 𝑥 squared. Negative four minus three equals negative seven. If you start at negative four on a number line and you subtract three, you’re moving to the left. And you’ll get to negative seven.
This expression is equivalent to three 𝑥 squared minus seven, which is option B. Option C has three 𝑥 squared minus one. This option has the mistake of saying negative four minus three is negative one. They’ve calculated negative four plus three instead of negative four minus three. There are also sign mistakes in option A and D.
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. 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. Option B is the only option that is equivalent to the expression 𝑥 squared minus four minus negative two 𝑥 squared plus three.