Factorize the following expression: (x^{4} - 256)

Question

Accepted Answer

Step:1 ：Recognize the expression as a difference of squares (a^{2} - b^{2}), where (a = x^{2}) and (b = 16)Step:2 ：Apply the difference of squares formula: (a^{2} - b^{2} = (a - b)(a + b)), therefore (x^{4} - 256 = (x^{2} - 16)(x^{2} + 16))Step:3 ：The term (x^{2} - 16) can be further factored using the difference of squares formula, where (a = x) and (b = 4), therefore (x^{2} - 16 = (x - 4)(x + 4))Step:4 ：Substitute this back into the expression to obtain the final factored form: (x^{4} - 256 = (x - 4)(x + 4)(x^{2} + 16))

Answer

Step: 1 ：Recognize the expression as a difference of squares (a^{2} - b^{2}), where (a = x^{2}) and (b = 16)Step: 2 ：Apply the difference of squares formula: (a^{2} - b^{2} = (a - b)(a + b)), therefore (x^{4} - 256 = (x^{2} - 16)(x^{2} + 16))Step: 3 ：The term (x^{2} - 16) can be further factored using the difference of squares formula, where (a = x) and (b = 4), therefore (x^{2} - 16 = (x - 4)(x + 4))Step: 4 ：Substitute this back into the expression to obtain the final factored form: (x^{4} - 256 = (x - 4)(x + 4)(x^{2} + 16))

Factorize the following expression: \(x^{4} - 256\)

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