randRange( 2, 9 ) randRange( 1, 9 ) A * A -B * B

Factor the following expression:

SQUAREx^2 + CONSTANT

^\s*$$\s*A\s*[xX]\s*\+\s*B\s*$$\s*$$\s*A\s*[xX]\s*[-\u2212]\s*B\s*$$\s*$^\s*$$\s*A\s*[xX]\s*[-\u2212]\s*B\s*$$\s*$$\s*A\s*[xX]\s*\+\s*B\s*$$\s*$
a factored expression, like (3x+1)(3x+2)

The expression is of the form \color{PINK}{a^2} - \color{BLUE}{b^2}, which is a difference of two squares so we can factor it as (\color{PINK}{a} + \color{BLUE}{b}) (\color{PINK}{a} - \color{BLUE}{b}).

What are the values of a and b?

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

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

Use the values we found for a and b to complete the factored expression, (\color{PINK}{a} + \color{BLUE}{b}) (\color{PINK}{a} - \color{BLUE}{b}).

So we can factor the expression as: (\color{PINK}{Ax} + \color{BLUE}{B}) (\color{PINK}{Ax} - \color{BLUE}{B})