Factorise: ${(x + 4 y)}^{2} - 4 z^{2}$

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Solution

Using the identity $a^{2} - b^{2} = (a + b) (a - b)$

By using the above identity, the equation $(x + 4 y)^{2} - 4 z^{2}$ can be factorised as follows:

$(x + 4 y)^{2} - 4 z^{2} = (x + 4 y)^{2} - (2 z)^{2} = (x + 4 y + 2 z) (x + 4 y - 2 z)$

Hence, $(x + 4 y)^{2} - 4 z^{2} = (x + 4 y + 2 z) (x + 4 y - 2 z)$

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