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Question

How do you factor $$x^4-16$$?


Solution

$$x^{4}-16=(x+2)(x-2)\left(x^{2}+4\right)$$

Explanation:

Recall the factor of difference of square $$a^{2}-b^{2}=(a-b)(a+b)$$

We can re-write 

$$x^{4}-16=\left(x^{2}\right)^{2}-4^{2}$$ 

$$\Rightarrow\left(x^{2}-4\right)\left(x^{2}+4\right)$$

$$\Rightarrow\left(x^{2}-2^{2}\right)(x+4) \Rightarrow$$ difference of square again 

$$\Rightarrow(x-2)(x+2)(x+4)$$

Mathematics

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