Question Video: Factorizing the Difference of Two Squares Mathematics • 9th Grade

Factorise fully 100๐‘ฅยฒ โˆ’ 121๐‘ฆยฒ.

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Video Transcript

Factorise fully 100๐‘ฅ squared minus 121๐‘ฆ 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 ๐‘Ž squared minus ๐‘ squared is equal to ๐‘Ž plus ๐‘ multiplied by ๐‘Ž minus ๐‘.

In this case, ๐‘Ž squared is equal to 100๐‘ฅ squared. Square rooting both sides of this equation gives us ๐‘Ž is equal to 10๐‘ฅ, as the square root of 100๐‘ฅ squared is 10๐‘ฅ. In the same way, ๐‘ squared is equal to 121 ๐‘ฆ squared. Square rooting both sides of this equation gives us ๐‘ is equal to 11๐‘ฆ.

This means that the full factorisation of 100๐‘ฅ squared minus 121๐‘ฆ squared is 10๐‘ฅ plus 11๐‘ฆ multiplied by 10๐‘ฅ minus 11๐‘ฆ. We could check this answer by expanding the two brackets, or parentheses, using the FOIL method.

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