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)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
yesterday

The difference of squares identity states that \( a^2 - b^2 = (a - b)(a + b) \).

To apply this to \( 13 \times 19 \), we can express this product in the form of a difference of squares. We notice that \( 16^2 = 256 \), which can be broken down into:

\[ 13 \times 19 = (16 - 3)(16 + 3) \]

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

\[ 16^2 - 3^2 = 256 - 9 = 247 \]

Therefore, \( 13 \times 19 \) can be rewritten using the difference of squares identity as:

(16−3)(16+3) \[ \text{(16 - 3)(16 + 3)} \]

This is the correct response.