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19 votes
Please Answer this as soon as possible.

Please Answer this as soon as possible.-example-1
User Sokid
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2 Answers

18 votes
18 votes

the first one

100x² + 20x +1

its a factor of different 2 squares

(10x - 1 )²

User Bluszcz
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17 votes
17 votes

Answer:

(c) 144x² -49y²

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.

User Xbd
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