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dangina [55]
3 years ago
11

How do I factor the difference of two squares

Mathematics
2 answers:
Dmitry [639]3 years ago
8 0

\bf x^4-16\implies x^{2\cdot 2}-4^2\implies (x^2)^2-4^2\implies (x^2-4)(x^2+4)
\\\\\\
(x^2-2^2)(x^2+4)\implies (x-2)(x+2)~~~~(x^2+4)

anastassius [24]3 years ago
3 0

Step-by-step explanation: If a variable is taken to an even power, that variable is a perfect square.

In this case, x^4 would therefore be a perfect square.

Since 16 is also a perfect square, what we

have here is the difference of two squares.

That can be factored as the product of two binomials,

one with a plus and one with a minus.

First ask yourself what are the factors of x^4 that are the same.

The rule is that those factors will use one-half

of the exponent on the original.

So the factors of x^4 that are the same are x^2 and

We place these in the first position of each binomial.

The factors of 16 that are the same are 4 and 4.

So our answer is (x^2 + 4)(x^2 - 4).

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