To determine the value of the given expression [tex]\((x + y)\left(x^2 + y^2 + xy\right)\)[/tex] when [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex], we'll follow these steps:
1. Substitute the given values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
[tex]\[
x = 2, \quad y = 3
\][/tex]
2. Calculate [tex]\(x + y\)[/tex]:
[tex]\[
x + y = 2 + 3 = 5
\][/tex]
3. Calculate [tex]\(x^2\)[/tex]:
[tex]\[
x^2 = 2^2 = 4
\][/tex]
4. Calculate [tex]\(y^2\)[/tex]:
[tex]\[
y^2 = 3^2 = 9
\][/tex]
5. Calculate [tex]\(xy\)[/tex]:
[tex]\[
xy = 2 \times 3 = 6
\][/tex]
6. Substitute these values into the expression [tex]\(x^2 + y^2 + xy\)[/tex]:
[tex]\[
x^2 + y^2 + xy = 4 + 9 + 6 = 19
\][/tex]
7. Multiply the results from steps 2 and 6:
[tex]\[
(x + y)\left(x^2 + y^2 + xy\right) = 5 \times 19 = 95
\][/tex]
Thus, the value of the expression [tex]\((x + y)\left(x^2 + y^2 + xy\right)\)[/tex] when [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex] is:
[tex]\[
95
\][/tex]
