Video: AQA GCSE Mathematics Higher Tier Pack 2 β€’ Paper 3 β€’ Question 14

Expand and fully simplify (π‘₯ βˆ’ 2𝑦)Β².

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Video Transcript

Expand and fully simplify π‘₯ minus two 𝑦 squared.

π‘₯ minus two 𝑦 squared equals π‘₯ minus two 𝑦 times itself. We’ll distribute the multiplication of π‘₯ minus two 𝑦: π‘₯ times π‘₯, π‘₯ times negative two 𝑦.

And then, we’ll do the same thing with our negative two 𝑦 term: negative two 𝑦 times π‘₯ and negative two 𝑦 times negative two 𝑦.

π‘₯ times π‘₯ equals π‘₯ squared. π‘₯ times negative two 𝑦 equals negative two π‘₯𝑦. Negative two 𝑦 times π‘₯ also equals negative two π‘₯𝑦. And finally, negative two 𝑦 times negative two 𝑦 equals positive four 𝑦 squared.

This form is expanded. However, it’s not fully simplified. There are some terms in here that can be combined. Negative two π‘₯𝑦 and negative two π‘₯𝑦 are like terms. They can be combined.

Negative two π‘₯𝑦 minus negative two π‘₯𝑦 equals negative four π‘₯𝑦. Bring down the π‘₯ squared. Bring down the four 𝑦 squared.

And our expanded, fully simplified form is π‘₯ squared minus four π‘₯𝑦 plus four 𝑦 squared.

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