Question

Write the product of 10.5 and 20.5 using the difference of two squares identity.(1 point) Responses (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) left parenthesis 15 point 5 plus 5 right parenthesis left parenthesis 15 point 5 minus 5 right parenthesis (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)

Answer 1

To find the product of \(10.5\) and \(20.5\) using the difference of two squares identity, we can express the numbers in a suitable form:

1. We note that \(10.5\) can be rewritten as \(15 - 4.5\) (or \(15.5 - 5\)) and \(20.5\) as \(15 + 5.5\) (or \(15.5 + 5\)).
2. We can use the identity \(a^2 - b^2 = (a+b)(a-b)\) in the form \(x^2 - y^2\).

Now set:

• \(a = 15.5\)
• \(b = 5\)

Then,

\[ 10.5 \cdot 20.5 = (15.5 - 5)(15.5 + 5) \]

This simplifies to:

\[ 10.5 \cdot 20.5 = (15.5 - 5)(15.5 + 5) = (15.5^2 - 5^2) \]

Calculating this gives:

\[ 15.5^2 = 240.25 \] \[ 5^2 = 25 \] \[ 10.5 \cdot 20.5 = 240.25 - 25 = 215.25 \]

So, the expression using the difference of two squares is \( (15.5 - 5)(15.5 + 5) \) which results in the same product.