Question Video: Factorizing the Difference of Two Squares Mathematics

Factorise fully 100π‘₯Β² βˆ’ 121𝑦².

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Video Transcript

Factorise fully 100π‘₯ squared minus 121𝑦 squared.

As both terms in the expression are square numbers, we can use the difference of two squares identity. The difference of two squares identity tells us that π‘Ž squared minus 𝑏 squared is equal to π‘Ž plus 𝑏 multiplied by π‘Ž minus 𝑏.

In this case, π‘Ž squared is equal to 100π‘₯ squared. Square rooting both sides of this equation gives us π‘Ž is equal to 10π‘₯, as the square root of 100π‘₯ squared is 10π‘₯. In the same way, 𝑏 squared is equal to 121 𝑦 squared. Square rooting both sides of this equation gives us 𝑏 is equal to 11𝑦.

This means that the full factorisation of 100π‘₯ squared minus 121𝑦 squared is 10π‘₯ plus 11𝑦 multiplied by 10π‘₯ minus 11𝑦. We could check this answer by expanding the two brackets, or parentheses, using the FOIL method.

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