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 plus π multiplied by π minus π, where π is the square root of the first term and π 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.
