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Jaime correctly factored x^4-12x^2y+36y^2 as (x^2-6y)^2. how did jaime find his answer?

1 Answer

3 votes

Answer:

by pattern matching

Explanation:

Jaime matched the terms of the expression to the terms of the expansion of the square of a binomial.

(a-b)^2 = a^2 -2ab +b^2

By recognizing that x^4 is a square, and that 36y^2 is a square, Jaime could assign a=x^2 and b=6y and then test to see if 2ab matches the middle term.

2ab = 2(x^2)(6y) = 12x^2y . . . . matches the middle term

This tells Jaime that his pattern recognition was right on, and that the factoring is ...

(x^2 -6y)^2

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