Question

How do you factor `4x^2+16x+16`?

Answer 1

`4x^2 + 16x + 16`

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a xxc = 4 xx 16 = 64`
and
`N_1 +N_2 = b = 16`

After trying out a few numbers we get `N_1 = 8` and `N_2 =8`
`8 xx 8 = 64`, and `8 +8= 16`

`4x^2 + 16x + 16 = 4x^2 + 8x +8x+ 16`
`= 4x (x + 2) +8 (x+2)`
`= (4x+8) (x + 2)`
The factor 4 is common to the terms in the first group above
`= {4(x+2)}(x+2)`
`=color(green)( {4(x+2)}(x+2))` is the Factorised form of `4x^2 + 16x + 16`