Answer :
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]
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]
