Question

often the sum of aquares cannot be factored, but x^4+4 can be factored, (add and subtract 4x^2) and the use factoring by grouping

Answer 1

Well, do it.

Answer 2

if i knew how to do it i would...

Answer 3

Not a helpful response.

Are you telling me you don't know how to subtract or add? That is what you are being asked to do. Please demonstrate.

Answer 4

yes, i can add and subtract. i shuold get x^4+4

Answer 5

and i have (x^2-2x+2)(x^2+2x+2) correct

Answer 6

You have \(x^4 + 4\)

You are asked to construct. \(x^4 + 4x^2 + 4 - 4x^2\)

You are then instructed to observe this grouping: \((x^4 + 4x^2 + 4) - 4x^2\)

Which is equivalent to \((x^2 + 2)^2 - (2x)^2\)

Finally observing that this factors as a difference of squares \(((x^2+2)+2x)((x^2+2)-2x)\)

This result is then simplified to what you have.

The problem statement just wants you to plod your way through the steps.