Question Video: Factorizing the Difference of Two Squares | Nagwa Question Video: Factorizing the Difference of Two Squares | Nagwa

Question Video: Factorizing the Difference of Two Squares Mathematics • Second Year of Preparatory School

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Factorise fully 100𝑥² − 121𝑦².

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Video Transcript

Factorise fully 100𝑥 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 𝑎 squared minus 𝑏 squared is equal to 𝑎 plus 𝑏 multiplied by 𝑎 minus 𝑏.

In this case, 𝑎 squared is equal to 100𝑥 squared. Square rooting both sides of this equation gives us 𝑎 is equal to 10𝑥, as the square root of 100𝑥 squared is 10𝑥. 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 100𝑥 squared minus 121𝑦 squared is 10𝑥 plus 11𝑦 multiplied by 10𝑥 minus 11𝑦. We could check this answer by expanding the two brackets, or parentheses, using the FOIL method.

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