Factorise:
$(4 x + 2 y)^{3} - (4 x - 2 y)^{3}$

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Solution

${(4 x + 2 y)}^{3} - {(4 x - 2 y)}^{3} a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2}) = (4 x + 2 y - 4 x + 2 y) [{(4 x + 2 y)}^{2} + (4 x + 2 y) (4 x - 2 y) + {(4 x - 2 y)}^{2}] = 4 y (48 x^{2} + 4 y^{2}) = 16 y [12 x^{2} + y^{2})$

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