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Sometimes we have quadratic equations of the form \({x^2}\) - a, in other words there is no term in \({x}\). Factorising these expressions is very straightforward if we recall that the expansion of (\({x}\) + \({y}\))(\({x}\) - \({y}\)) = \({x^2}\) - \({y^2}\)

Factorise \({x^2}\) - 64

Recalling (\({x}\) + \({y}\))(\({x}\) - \({y}\)) = \({x^2}\) - \({y^2}\) in our expression \({y^2}\) = 64 and therefore \({y}\) is the square root of 64 which is 8. Similarly we square root \({x^2}\) to obtain \({x}\).

It should hopefully be easy to see that \({x^2}\) - 64 = (\({x}\) + 8)(\({x}\) - 8).