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Difference of squares gives which complex factors for the expression x^2+13
a. (x - i sqr 13)(x - i sqr 13)
b. (x + 13i)^2(X - 13i)^2
c.(x + i sqr 13)(x - i sqr 13)
d. (x + 13i)(X - 13i)


ASAP pls

Respuesta :

The Given Expression is : → x² + 13

  =  x² + (√13)²

=  x² - ( i √13)²  As , i²= -1 because , i = √-1

= (x - i√13)(x +√13)   → Using the formula , A² - B² = (A-B)(A+B)

Out of the four options Given : Option C →(x - i√13)(x +√13) is true regarding the expansion of function x² + 13.

Answer:

Option C.

Step-by-step explanation:

Shortest way to solve this question is to find the factors of the given expression.

The given expression is (x² + 13).

Now we have to factorize it.

(x² + 13) = x² + (√13)²

             = x² + [-(i)²√(13)²]  [Since i = √(-1)]

             = x² - (i√13)²

             = (x - i√3)(x + i√3) [Since (a² - b²) = (a + b)(a - b)]

Option C will be the answer.

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