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in Algebraic Expressions by (26.3k points)
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The expression x4 + 4 can be factorized as

A. (x2 + 2x + 2)(x2 - 2x + 2) 

B. (x2 + 2x + 2)(x2 + 2x - 2) 

C. (x2 - 2x - 2)(x2 - 2x + 2) 

D. (x2 + 2)(x2 - 2)

1 Answer

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Best answer

We have ,

\(=\text{x}^{4}+4\)

\(=\text{x}^{4}+4\text{x}^{2}+4-4\text{x}^{2}\)

\(=(\text{x}^{2}+2)^{2}-4\text{x}^{2}\)

\(=(\text{x}^{2}+2)^{2}-(2\text{x})^{2}\)

[\(\text{x}^{2}-\text{y}^{2}=(\text{x}-\text{y})(\text{x+y})]\) 

\(=(\text{x}^{2}+2+2\text{x})(\text{x}^{2}+2-2\text{x})\)

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