# How do you factor #16x^2+8x+1#?

##### 1 Answer

Dec 24, 2016

#### Answer:

#### Explanation:

Notice that:

#1681 = 41^2#

Hence we find:

#16x^2+8x+1 = (4x+1)^2#

Was that a bit fast? Think what happens when we put

#16x^2+8x+1 = 16(10)^2+8(10)+1 = 1600+80+1 = 1681#

#4x+1 = 4(10)+1 = 40+1 = 41#

When we square

Another way we could spot this is as follows:

Notice that both

#(4x+1)^2 = (4x)^2+2(4x)(1)+1^2 = 16x^2+8x+1" "# - Yes.

In general:

#(a+b)^2 = a^2+2ab+b^2#

So if we can identify