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x⁴-(x-2)⁴

Consider the expression, x^{4} - {(x - 2)}^{4} Use mathematical identity : a^{2} - b^{2} = (a - b) (a + b) Therefore, the given expression reduces to x^{4} - {(x - 2)}^{4} = (x^{2} + {(x - 2)}^{2}) (x^{2} - {(x - 2)}^{2}) = (x^{2} + {(x - 2)}^{2}) (x - (x - 2)) (x + (x - 2)) = (x^{2} + x^{2} + 4 - 4 x) (2) (2 x - 2) = 2 (2 x^{2} + 4 - 4 x) (2 x - 2)

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