Answer:
(c) 144x² -49y²
Step-by-step explanation:
In order for the pattern for factoring the difference of squares to apply, the expression must be a binomial whose terms are squares and whose value is their difference.
Evaluating choices
A. 100x² +20x +1 = (10x +1)² . . . . . it is a square, not the difference of squares
B. x² +4x -12 = (x² +4x +4) -16 = (x +2)² -4² . . . . can be written as the difference of squares (see comment below)
C. 144x² -49y² = (12x)² -(7y)² . . . . the difference of squares
D. 14x -16 = 14x -4² . . . . first term is not a square.
The answer choice that matches the pattern "difference of squares" is ...
144x² -49y²
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Additional comment
Virtually any quadratic that is not a perfect square can be written in a way that would allow it to be factored as the difference of squares. (This is what we do when we "complete the square.) Answer choice B is an example of this. If the "difference of squares" factoring were expanded in that case, it would look like ...
= (x+2 +4)(x+2 -4) = (x +6)(x -2)
This doesn't really match the pattern (a +b)(a -b), so the trinomial given in the answer choice is not really a candidate for factoring using the difference of squares pattern for a binomial.
