To find the value of [tex]\((x - y)(x - y)\)[/tex], which can be denoted as [tex]\((x - y)^2\)[/tex], we can utilize the given information and a helpful algebraic identity.
Given:
[tex]\(xy = 3\)[/tex]
[tex]\(x^2 + y^2 = 25\)[/tex]
We use the identity for the square of a difference, which is given by:
[tex]\[
(x - y)^2 = x^2 - 2xy + y^2
\][/tex]
Now, we substitute the given values into this identity.
1. Substitute [tex]\(x^2 + y^2\)[/tex] with 25:
[tex]\[
(x - y)^2 = x^2 + y^2 - 2xy
\][/tex]
2. Substitute [tex]\(xy\)[/tex] with 3:
[tex]\[
(x - y)^2 = 25 - 2 \cdot 3
\][/tex]
3. Perform the multiplication in the equation:
[tex]\[
(x - y)^2 = 25 - 6
\][/tex]
4. Subtract 6 from 25:
[tex]\[
(x - y)^2 = 19
\][/tex]
Hence, the value of [tex]\((x - y)(x - y)\)[/tex] is:
[tex]\[
\boxed{19}
\][/tex]
