+0

+3
124
2
+7

Factor this expression

x+10x+25

ManuelBautista3445  Nov 20, 2017
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#1
+394
+3

Factor:

\(x2 + 10x + 25\)

First we can rewrite 25 to 52 and we will check the middle term by multiplying 2ab. This is factoring by the perfect square rule.  Now we can check the result of this new problem compared to the original expression.

We now have \(2ab = 2*x*5 = 0\)

Simplify this to \(2ab = 10x =0\)

Now we factor by the perfect square trinomial rule  [  \(a2+2ab+b2=(a+b)2a2+2ab+b2=(a+b)2\) where \( a=xa=x \) and \(b=5b=5.\) ]  to get: \(( x + 5 ) 2 = 0\).

Next we can set \(x+5\) equal to 0 and solve for \(x \).

Set the factor equal to 0 and we get: \(x+5=0\)

Solve that and you get  x = -5

Mr.Owl  Nov 20, 2017
#2
+84167
+4

This is a perfect square trinomial

We're looking for two integers that sum to 10  and multiply to 25

5    and   5    are just what we need

So.....factor as

(x + 5) ( x+ 5)  =   (x + 5)^2

CPhill  Nov 20, 2017

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