How can 13×19 be rewritten using the difference of two squares identity?(1 point)

Responses

(10+3)(22−3)
left parenthesis 10 plus 3 right parenthesis left parenthesis 22 minus 3 right parenthesis

(13−3)(19+3)
left parenthesis 13 minus 3 right parenthesis left parenthesis 19 plus 3 right parenthesis

(16−3)(16+3)
left parenthesis 16 minus 3 right parenthesis left parenthesis 16 plus 3 right parenthesis

(11−3)(11+3)

1 answer

The difference of squares identity states that a2b2=(ab)(a+b).

To apply this to 13×19, we can express this product in the form of a difference of squares. We notice that 162=256, which can be broken down into:

13×19=(163)(16+3)

This allows us to use a=16 and b=3, resulting in:

16232=2569=247

Therefore, 13×19 can be rewritten using the difference of squares identity as:

(16−3)(16+3) (16 - 3)(16 + 3)

This is the correct response.