How do you factor completely $4 x^{2} - 25$ $4x^2-25$ ?

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How do you factor completely $4 x^{2} - 25$ $4x^2-25$ ?

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Answer 1 · 2015-11-15T05:05:56

$(2 x + 5) (2 x - 5)$ $(2x+5)(2x-5)$

Explanation:

Realize that $4 x^{2} - 25$ $4x^2-25$ is a difference of squares. Differences of squares, such as $a^{2} - b^{2}$ $a^2-b^2$ , can be factored into $(a + b) (a - b)$ $(a+b)(a-b)$ .

Since $4 x^{2} = {(2 x)}^{2}$ $4x^2=(2x)^2$ and $25 = {(5)}^{2}$ $25=(5)^2$ , we can say that $4 x^{2} - 25 = (2 x + 5) (2 x - 5)$ $4x^2-25=color(blue)((2x+5)(2x-5)$ .

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How do you factor completely $4 x^{2} - 25$ $4x^2-25$ ?

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