How do you factor $x^{2} - 4 x + 4$ $x^2-4x+4$ using the perfect squares formula?

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How do you factor $x^{2} - 4 x + 4$ $x^2-4x+4$ using the perfect squares formula?

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Answer 1 · 2017-05-03T13:59:18

$x^{2} - 4 x + 4 = {(x - 2)}^{2}$ $x^2-4x+4=(x-2)^2$

Explanation:

I think what is being referred to is the relationship:

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $(a+b)^2=a^2+2ab+b^2$

We've been given the equation $x^{2} - 4 x + 4$ $x^2-4x+4$ - let's factor using the above relationship.

We can take the $x^{2}$ $x^2$ term and therefore assign $x = a$ $x=a$ . We can also see that the $+ 4$ $+4$ can be assigned to the $b^{2}$ $b^2$ term, giving $b = \pm 2$ $b=pm2$ .

Lastly, we can take the $- 4 x$ $-4x$ term, assign it to the $+ 2 a b$ $+2ab$ and say:

$- 4 x = 2 a b$ $-4x=2ab$

$- 2 x = a b$ $-2x=ab$

We can substitute $x$ $x$ in for $a$ $a$ :

$- 2 x = x b$ $-2x=xb$

$- 2 = b$ $-2=b$

and this tells us we will use $b = - 2$ $b=-2$ and not $b = 2$ $b=2$ .

All in all, we'll get:

$x^{2} - 4 x + 4 = {(x - 2)}^{2}$ $x^2-4x+4=(x-2)^2$

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How do you factor $x^{2} - 4 x + 4$ $x^2-4x+4$ using the perfect squares formula?

1 Answer

Explanation:

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