# Video: US-SAT03S3-Q01-714186467212

Consider the expression (4𝑥³𝑦² − 5𝑥²𝑦 − 2𝑥³𝑦²) − (−2𝑥𝑦² − 5𝑥²𝑦). Which of the following is equivalent to this expression? [A] 2 𝑥³ 𝑦² − 2𝑥𝑦². [B] 2 𝑥³ 𝑦² − 10𝑥²𝑦 + 2 𝑥𝑦². [C] 2 𝑥³ 𝑦² − 10𝑥²𝑦 − 2 𝑥𝑦². [D] 2 𝑥³ 𝑦² + 2 𝑥𝑦².

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### Video Transcript

Consider the expression four 𝑥 cubed 𝑦 squared minus five 𝑥 squared 𝑦 minus two 𝑥 cubed 𝑦 squared minus negative two 𝑥𝑦 squared minus five 𝑥 squared 𝑦. Which of the following is equivalent to this expression? a) Two 𝑥 cubed 𝑦 squared minus two 𝑥𝑦 squared. b) Two 𝑥 cubed 𝑦 squared minus 10𝑥 squared 𝑦 plus two 𝑥𝑦 squared. c) Two 𝑥 cubed 𝑦 squared minus 10𝑥 squared 𝑦 minus two 𝑥𝑦 squared. Or d) two 𝑥 cubed 𝑦 squared plus two 𝑥𝑦 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 𝑥 cubed 𝑦 squared. We also have two 𝑥 cubed 𝑦 squared. We combine these two like terms by combining their coefficients. We have four 𝑥 cubed 𝑦 squared and we’re subtracting two 𝑥 cubed 𝑦 squared. Four minus two is two. So combining these like terms will give us two 𝑥 cubed 𝑦 squared. From there, we’ll just bring everything else down.

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