Question

How do you factor a perfect square trinomial `36b^2 − 24b + 16`?

Answer 1

We know that `(color(blue)a-color(red)b)²=color(blue)(a^2)-2color(blue)acolor(red)b+color(red)(b²)`

`36b^2=color(blue)((6b)²)=color(blue)(a^2)` ( `color(blue)(a=6b` )
`16=color(red)(4^2)=color(red)(b^2)` ( `color(red)(b=4` )

We are going to check if `-2ab=-24b` :
`-2ab=-2*6b*4=-48b` : incorrect

Thus `36b^2-24b+16` is not a perfect square.