# Video: US-SAT03S3-Q01-714186467212

Consider the expression (4π₯Β³π¦Β² β 5π₯Β²π¦ β 2π₯Β³π¦Β²) β (β2π₯π¦Β² β 5π₯Β²π¦). Which of the following is equivalent to this expression? [A] 2 π₯Β³ π¦Β² β 2π₯π¦Β². [B] 2 π₯Β³ π¦Β² β 10π₯Β²π¦ + 2 π₯π¦Β². [C] 2 π₯Β³ π¦Β² β 10π₯Β²π¦ β 2 π₯π¦Β². [D] 2 π₯Β³ π¦Β² + 2 π₯π¦Β².

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### Video Transcript

Consider the expression four π₯ cubed π¦ squared minus five π₯ squared π¦ minus two π₯ cubed π¦ squared minus negative two π₯π¦ squared minus five π₯ squared π¦. Which of the following is equivalent to this expression? a) Two π₯ cubed π¦ squared minus two π₯π¦ squared. b) Two π₯ cubed π¦ squared minus 10π₯ squared π¦ plus two π₯π¦ squared. c) Two π₯ cubed π¦ squared minus 10π₯ squared π¦ minus two π₯π¦ squared. Or d) two π₯ cubed π¦ squared plus two π₯π¦ squared.

To try and simplify this expression, we want to see if there are any like terms. Like terms have the same variable taken to the same power. We have four π₯ cubed π¦ squared. We also have two π₯ cubed π¦ squared. We combine these two like terms by combining their coefficients. We have four π₯ cubed π¦ squared and weβre subtracting two π₯ cubed π¦ squared. Four minus two is two. So combining these like terms will give us two π₯ cubed π¦ squared. From there, weβll just bring everything else down.

Since weβre subtracting something inside the brackets, we need to distribute this subtraction. Weβre subtracting negative two π₯π¦ squared. We can rewrite that to say plus two π₯π¦ squared. Weβre also subtracting negative five π₯ squared π¦. And we can rewrite that as adding five π₯ squared π¦. We can bring down the rest of our equation, look again for any like terms. π₯ squared π¦ and π₯ squared π¦ are like terms. We combine these like terms by combining their coefficient. Negative five π₯ squared π¦ plus five π₯ squared π¦ will cancel out, leaving you with two π₯ cubed π¦ squared plus two π₯π¦ squared, option d.