Question

How do you factor the expression `c^2 + 4c + 4`?

Answer 1

`c^2+4x+4=color(green)((c+2)(c+2))`

Explanation:

Since `(c+m)(c+n)=c^2+(m+n)c+mn`

we are looking for factors (`m` and `n`) of `4` which add up to `4`

Factors of `4`
`color(white)("XXX")1xx4` but `1+4!=4`
`color(white)("XXX")2xx2` and `2xx2=4` Hooray! we've found our pair.