Video: US-SAT03S3-Q01-714186467212

Consider the expression (4π‘₯³𝑦² βˆ’ 5π‘₯²𝑦 βˆ’ 2π‘₯³𝑦²) βˆ’ (βˆ’2π‘₯𝑦² βˆ’ 5π‘₯²𝑦). Which of the following is equivalent to this expression? [A] 2 π‘₯Β³ 𝑦² βˆ’ 2π‘₯𝑦². [B] 2 π‘₯Β³ 𝑦² βˆ’ 10π‘₯²𝑦 + 2 π‘₯𝑦². [C] 2 π‘₯Β³ 𝑦² βˆ’ 10π‘₯²𝑦 βˆ’ 2 π‘₯𝑦². [D] 2 π‘₯Β³ 𝑦² + 2 π‘₯𝑦².

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Video Transcript

Consider the expression four π‘₯ cubed 𝑦 squared minus five π‘₯ squared 𝑦 minus two π‘₯ cubed 𝑦 squared minus negative two π‘₯𝑦 squared minus five π‘₯ squared 𝑦. Which of the following is equivalent to this expression? a) Two π‘₯ cubed 𝑦 squared minus two π‘₯𝑦 squared. b) Two π‘₯ cubed 𝑦 squared minus 10π‘₯ squared 𝑦 plus two π‘₯𝑦 squared. c) Two π‘₯ cubed 𝑦 squared minus 10π‘₯ squared 𝑦 minus two π‘₯𝑦 squared. Or d) two π‘₯ cubed 𝑦 squared plus two π‘₯𝑦 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 𝑦 squared. We also have two π‘₯ cubed 𝑦 squared. We combine these two like terms by combining their coefficients. We have four π‘₯ cubed 𝑦 squared and we’re subtracting two π‘₯ cubed 𝑦 squared. Four minus two is two. So combining these like terms will give us two π‘₯ 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 π‘₯𝑦 squared. We can rewrite that to say plus two π‘₯𝑦 squared. We’re also subtracting negative five π‘₯ squared 𝑦. And we can rewrite that as adding five π‘₯ squared 𝑦. We can bring down the rest of our equation, look again for any like terms. π‘₯ squared 𝑦 and π‘₯ squared 𝑦 are like terms. We combine these like terms by combining their coefficient. Negative five π‘₯ squared 𝑦 plus five π‘₯ squared 𝑦 will cancel out, leaving you with two π‘₯ cubed 𝑦 squared plus two π‘₯𝑦 squared, option d.

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