Factorise fully 64𝑥 squared minus 81.
We can factorise this equation using the difference of two squares method. This will give us two brackets or parentheses: 𝑎 plus 𝑏 multiplied by 𝑎 minus 𝑏, where 𝑎 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 64𝑥 squared is eight 𝑥 as eight 𝑥 multiplied by eight 𝑥 gives us 64𝑥 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 𝑥 plus nine and eight 𝑥 minus nine.
As a result of this, we can say when factorising fully the expression 64𝑥 squared minus 81. The answer is eight 𝑥 plus nine multiplied by eight 𝑥 minus nine.
We can check this answer using the FOIL method to expand the two parentheses. Multiplying the first terms, eight 𝑥 multiplied by eight 𝑥 gives us 64𝑥 squared. Multiplying the outside terms gives us negative 72𝑥. Multiplying the inside terms gives us positive 72𝑥. And finally, multiplying the last terms gives us negative 81.
As negative 72𝑥 plus 72𝑥 equal zero, we can see that our answer is 64𝑥 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 64𝑥 squared minus 81 is equal to eight 𝑥 plus nine multiplied by eight 𝑥 minus nine.