Answer :

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].