To find the value of the expression [tex]\(2 x^2 y + 4 y^2\)[/tex] when [tex]\(x = -1\)[/tex] and [tex]\(y = 3\)[/tex], follow these steps:
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
[tex]\[
2 (-1)^2 (3) + 4 (3)^2
\][/tex]
2. Calculate [tex]\((-1)^2\)[/tex]:
[tex]\[
(-1)^2 = 1
\][/tex]
So the expression becomes:
[tex]\[
2 (1) (3) + 4 (3)^2
\][/tex]
3. Multiply [tex]\(2 \times 1 \times 3\)[/tex]:
[tex]\[
2 \times 1 \times 3 = 6
\][/tex]
Now the expression is:
[tex]\[
6 + 4 (3)^2
\][/tex]
4. Calculate [tex]\(3^2\)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
So the expression becomes:
[tex]\[
6 + 4 (9)
\][/tex]
5. Multiply [tex]\(4 \times 9\)[/tex]:
[tex]\[
4 \times 9 = 36
\][/tex]
Now the expression is:
[tex]\[
6 + 36
\][/tex]
6. Add 6 and 36:
[tex]\[
6 + 36 = 42
\][/tex]
Therefore, the value of [tex]\(2 x^2 y + 4 y^2\)[/tex] when [tex]\(x = -1\)[/tex] and [tex]\(y = 3\)[/tex] is [tex]\(42\)[/tex].
