Question Video: Factorizing the Difference of Two Squares

Factorise fully 64π‘₯Β² βˆ’ 81.

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Video Transcript

Factorise fully 64π‘₯ squared minus 81.

We can factorise this equation using the difference of two squares method. This will give us two brackets or parentheses: π‘Ž plus 𝑏 multiplied by π‘Ž minus 𝑏, where π‘Ž is the square root of the first term and 𝑏 is the square root of the second term in our equation.

The square root of 64π‘₯ squared is eight π‘₯ as eight π‘₯ multiplied by eight π‘₯ gives us 64π‘₯ squared. Likewise, the square root of 81 is equal to nine as nine multiplied by nine equals 81. This means that our two brackets or parentheses will be eight π‘₯ plus nine and eight π‘₯ minus nine.

As a result of this, we can say when factorising fully the expression 64π‘₯ squared minus 81. The answer is eight π‘₯ plus nine multiplied by eight π‘₯ minus nine.

We can check this answer using the FOIL method to expand the two parentheses. Multiplying the first terms, eight π‘₯ multiplied by eight π‘₯ gives us 64π‘₯ squared. Multiplying the outside terms gives us negative 72π‘₯. Multiplying the inside terms gives us positive 72π‘₯. And finally, multiplying the last terms gives us negative 81.

As negative 72π‘₯ plus 72π‘₯ equal zero, we can see that our answer is 64π‘₯ squared minus 81. As this is the same equation as we started with, we can see that our answer was correct. The full factorisation of 64π‘₯ squared minus 81 is equal to eight π‘₯ plus nine multiplied by eight π‘₯ minus nine.

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