# Video: AQA GCSE Mathematics Higher Tier Pack 2 • Paper 3 • Question 14

Expand and fully simplify (𝑥 − 2𝑦)².

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### Video Transcript

Expand and fully simplify 𝑥 minus two 𝑦 squared.

𝑥 minus two 𝑦 squared equals 𝑥 minus two 𝑦 times itself. We’ll distribute the multiplication of 𝑥 minus two 𝑦: 𝑥 times 𝑥, 𝑥 times negative two 𝑦.

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

𝑥 times 𝑥 equals 𝑥 squared. 𝑥 times negative two 𝑦 equals negative two 𝑥𝑦. Negative two 𝑦 times 𝑥 also equals negative two 𝑥𝑦. 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 𝑥𝑦 and negative two 𝑥𝑦 are like terms. They can be combined.

Negative two 𝑥𝑦 minus negative two 𝑥𝑦 equals negative four 𝑥𝑦. Bring down the 𝑥 squared. Bring down the four 𝑦 squared.

And our expanded, fully simplified form is 𝑥 squared minus four 𝑥𝑦 plus four 𝑦 squared.