How do you factor $1 - 4 y^{2}$ $1 - 4y^2$ ?

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How do you factor $1 - 4 y^{2}$ $1 - 4y^2$ ?

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Answer 1 · 2018-03-03T09:25:45

$(1 - 2 y) (1 + 2 y)$ $(1-2y)(1+2y)$

Explanation:

$this is a difference of squares$ $"this is a "color(blue)"difference of squares"$

$∙ x a^{2} - b^{2} = (a - b) (a + b)$ $•color(white)(x)a^2-b^2=(a-b)(a+b)$

$here a = 1 and b = 2 y$ $"here "a=1" and "b=2y$

$\Rightarrow 1 - 4 y^{2} = (1 - 2 y) (1 + 2 y)$ $rArr1-4y^2=(1-2y)(1+2y)$

Answer 2 · 2018-03-03T09:27:32

$(1 + 2 y) (1 - 2 y)$ $(1+2y)(1-2y)$

Explanation:

$1 - 4 y^{2}$ $color(blue)(1-4y^2)$

$\Rightarrow {(1)}^{2} - {(2 y)}^{2}$ $=>color(blue)((1)^2 - (2y)^2)$

We have an identity for $a^{2} - b^{2}$ $color(green)(a^2 - b^2)$ which is equal to $(a + b) (a - b)$ $color(green)((a+b)(a-b))$ .

So , ${(1)}^{2} - {(2 y)}^{2}$ $color(red)((1)^2 - (2y)^2)$

$\Rightarrow (1 + 2 y) (1 - 2 y)$ $=> color(red)((1+2y)(1-2y))$

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