Factor Completely: 25x2 - 64 A) 5(x - 8)(x + 8) B) 5(x - 8)(x - 8) C) (5x - 8)(5x + 8) D) (25x - 1)(x + 64)

Mathematics

1 answer:

ZanzabumX [31]3 years ago

4 0

Rewrite it in the form a^2 - b^2, where a = 5x and b = 8

(5x)^2 - 8^2

Use the Difference of Squares; a^2 - b^2 = (a + b)(a - b)

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Hello, please consider the following.

We will multiply the numerator and denominator by

$4+\sqrt{6x}$

to get rid of the root in the denominator.

First of all, we cannot divide by 0, right? So, we need to make sure that the denominator is different from 0.

$4-\sqrt{6x} =0\sqrt{6x}=4\\\\\text{Take the square}\\\\6x=4^2=16\\\\x=\dfrac{16}{6}=\dfrac{8}{3}$

We need to take any x real number different from 8/3 then and simplify the expression.

Let's do it!

$\begin{aligned}\dfrac{4}{4-\sqrt{6x}}&=\dfrac{4(4+\sqrt{6x})}{(4+\sqrt{6x})(4-\sqrt{6x})}\\\\&=\dfrac{4(4+\sqrt{6x})}{(4^2-\sqrt{6x}^2)}\\\\&=\dfrac{4(4+\sqrt{6x})}{(16-6x)}\\\\&=\dfrac{2(4+\sqrt{6x})}{(8-3x)}\\\\&\large \boxed{=\dfrac{8+2\sqrt{6x}}{8-3x}}\end{aligned}$