Write the product of 10.5 and 20.5 using the difference of two squares identity.(1 point)

Question

Responses

(15.5−5)(25.5−5)
left parenthesis 15 point 5 minus 5 right parenthesis left parenthesis 25 point 5 minus 5 right parenthesis

(5.5+5)(20.5−5)
left parenthesis 5 point 5 plus 5 right parenthesis left parenthesis 20 point 5 minus 5 right parenthesis

(15.5+5)(5.5+5)
left parenthesis 15 point 5 plus 5 right parenthesis left parenthesis 5 point 5 plus 5 right parenthesis

(15.5+5)(15.5−5)

Answer 1

To express the product of 10.5 and 20.5 using the difference of two squares identity, we can rewrite these numbers:

• Let's denote \(x = 15.5\) (which is the midpoint between 10.5 and 20.5).
• Then, we express 10.5 as \(x - 5\) and 20.5 as \(x + 5\).

The product can then be written as: \[ (x - 5)(x + 5) \]

According to the difference of squares identity, this product is equal to: \[ x^2 - 5^2 \]

Substituting back in for \(x\): \[ (15.5 - 5)(15.5 + 5) \]

Thus, the correct response is: \[ (15.5 + 5)(15.5 - 5) \]