randRange(2, 6) randRange(1, 6) randFromArray([2, 3, 5]) A * A -B * B

Factor the expression below completely. All coefficients should be integers.

F * SQUAREx^2 + F * CONSTANT

F(Ax + B)(Ax - B)

We can start by factoring a \green{F} out of each term:

\qquad \green{F}(\pink{SQUAREx^2} - \blue{abs(CONSTANT)})

The second term is of the form \pink{a^2} - \blue{b^2}, which is a difference of two squares so we can factor it as \green{F}(\pink{a} + \blue{b})(\pink{a} - \blue{b}).

What are the values of \pink{a} and \blue{b}?

\qquad \pink{a = \sqrt{SQUAREx^2} = Ax}

\qquad \blue{b = \sqrt{B * B} = B}

Use the values we found for \pink{a} and \blue{b} to complete the factored expression, \green{F}(\pink{a} + \blue{b})(\pink{a} - \blue{b}).

So we can factor the expression as: \green{F}(\pink{Ax} + \blue{B}) (\pink{Ax} - \blue{B})