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Kathy wants to factor x2 – 12x + 36 by grouping; however, Tom says it is a special product and can factor a different way. Using complete sentences explain and demonstrate how both methods will result in the same factors.
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Kathy wants to replace -12x with -6x-6x so she will have:
She will then group the first two terms and the last two terms using the associative property to get:
The first two terms have the common factor x. The last two terms have the common factor -6.
Kathy will factor those out and get:
She now has an expression with two terms. The two terms have the common factor x-6.
Factoring it out, Kathy has: (x-6)(x-6).
Tom recognizes that x^2-12x+36 is of the form a^2-2ab +b^2 whose factors are (a-b)^2 where a = x and b = 6. He replaces a with x and b with 6 to get the factors (x-6)^2.