Factor completely 25x2 − 36.

Mathematics

2 answers:

Ivenika [448]3 years ago

6 0

25x² - 36
25x² + 30x - 30x - 36
5x(5x) + 5x(6) - 6(5x) - 6(6)
5x(5x + 6) - 6(5x + 6)
(5x - 6)(5x + 6)

The answer is C.

kondaur [170]3 years ago

5 0

Answer:

Option (3) is correct.

The factored form of given equation $25x^2-36$ is $(5x+6)(5x-6)$

Step-by-step explanation:

Given : equation $25x^2-36$

We have to factorize the given equation completely.

Consider the given equation $25x^2-36$

Using algebraic identity $a^2-b^2=(a+b)(a-b)$

We have ,

$25x^2-36$ can be written as $(5x)^2-(6)^2$

Applying above idenity, we have,

$(5x)^2-(6)^2=(5x+6)(5x-6)$

Thus, the factored form of given equation $25x^2-36$ is $(5x+6)(5x-6)$

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Answer:

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Step-by-step explanation:

$\displaystyle ax^2+bx+c=0\\\\ax^2+bx=-c\\\\x^2+\biggr(\frac{b}{a}\biggr)x=-\frac{c}{a}\\\\x^2+\biggr(\frac{b}{a}\biggr)x+\biggr(\frac{b}{2a}\biggr)^2=-\frac{c}{a}+\biggr(\frac{b}{2a}\biggr)^2\\\\x^2+\biggr(\frac{b}{a}\biggr)x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}\\ \\\biggr(x+\frac{b}{2a}\biggr)^2=-\frac{4ac}{4a^2}+\frac{b^2}{4a^2}\\ \\\biggr(x+\frac{b}{2a}\biggr)^2=\frac{b^2-4ac}{4a^2}\\ \\x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$