Pictures can help find factoring patterns, but some factoring patterns are easy to recognize looking at the algebraic expression.
Multiply: What do you notice about the products?
\((x + 2)(x – 2)\)
\((x – 5)(x + 5)\)
\((a + b)(a – b)\)
Factor: Use what you know about the products
\(x^2 – 16\)
\(25x^2 – 1\)
Notice the special factoring patterns is the difference of squares:
\(a^2 – b^2 = (a + b)(a – b)\) or \((a – b)(a + b)\).
One of the two expressions in the activity you just did is written as the difference of two squares. Determine which one it is and factor using the pattern above. How does this connect to the other representations of this expression?
Did you recognize the expression \((n+2)^2-4\) or in an equivalent form [(n+2)+2][(n+2)-2]?
What is the same expression in its simplified form?
Did you notice any other patterns in the diagrams? If so, what did you notice?