# publicKhan/khan-exercises

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randRange( 2, 6 )                    randRange( 1, 6 )                    randFromArray([2, 3, 5])                    A * A                    -B * B                    F                    "[-\\u2212]" + F                    "\$$\\s*" + A + "\\s*[xX]\\s*\\+\\s*" + B + "\\s*\$$"                    "\$$\\s*[-\\u2212]" + A + "\\s*[xX]\\s*[-\\u2212]\\s*" + B + "\\s*\$$"                    "\$$\\s*" + A + "\\s*[xX]\\s*[-\\u2212]\\s*" + B + "\\s*\$$"                    "\$$\\s*[-\\u2212]" + A + "\\s*[xX]\\s*\\+\\s*" + B + "\\s*\$$"

Factor the following expression:

F * SQUAREx^2 + F * CONSTANT

^\s*TERM1\s*TERM2\s*TERM3\s*$^\s*TERM1\s*TERM3\s*TERM2\s*$

^\s*TERM2\s*TERM1\s*TERM3\s*$^\s*TERM2\s*TERM3\s*TERM1\s*$

^\s*TERM3\s*TERM1\s*TERM2\s*$^\s*TERM3\s*TERM2\s*TERM1\s*$

^\s*TERM1N\s*TERM2N\s*TERM3\s*$^\s*TERM1N\s*TERM3N\s*TERM2\s*$

^\s*TERM2N\s*TERM1N\s*TERM3\s*$^\s*TERM2N\s*TERM3N\s*TERM1\s*$

^\s*TERM3N\s*TERM1N\s*TERM2\s*$^\s*TERM3N\s*TERM2N\s*TERM1\s*$

^\s*TERM1N\s*TERM2\s*TERM3N\s*$^\s*TERM1N\s*TERM3\s*TERM2N\s*$

^\s*TERM2N\s*TERM1\s*TERM3N\s*$^\s*TERM2N\s*TERM3\s*TERM1N\s*$

^\s*TERM3N\s*TERM1\s*TERM2N\s*$^\s*TERM3N\s*TERM2\s*TERM1N\s*$

^\s*TERM1\s*TERM2N\s*TERM3N\s*$^\s*TERM1\s*TERM3N\s*TERM2N\s*$

^\s*TERM2\s*TERM1N\s*TERM3N\s*$^\s*TERM2\s*TERM3N\s*TERM1N\s*$

^\s*TERM3\s*TERM1N\s*TERM2N\s*$^\s*TERM3\s*TERM2N\s*TERM1N\s*$

a factored expression, like 2(3x+1)(3x+2)

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

The second term 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                        \green{F}(\pink{a} + \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,                        \green{F}(\color{PINK}{a} + \color{BLUE}{b})                        (\color{PINK}{a} - \color{BLUE}{b}).

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

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