Question

In Algebra you learned that Difference of Perfect Squares is x^2 - 25 = (x+5)(x-5)

Is there a way to factor the sum of perfect squares? ex: x^2 + 25 = (?)(?)

Answer 1

dd4l

Explanation:

yup

Answer 2

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Answer:

yes, if you allow complex numbers; no, if you don't

Explanation:

The sum of squares can be considered to be the difference of squares, where one of the squares is negative. The negative square is the square of an imaginary number, so the factoring involves imaginary numbers.

x^2 +25 = x^2 - (-25) = x^2 -(5i)^2

= (x -5i)(x +5i) . . . . factoring in the complex numbers

There is no factoring in real numbers.