To find the value of the expression [tex]\(2a^2 + 5b^2\)[/tex] when [tex]\(a = -6\)[/tex] and [tex]\(b = 2\)[/tex], follow these steps:
1. Substitute the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- [tex]\(a = -6\)[/tex]
- [tex]\(b = 2\)[/tex]
2. Square the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
- [tex]\(a^2 = (-6)^2 = 36\)[/tex]
- [tex]\(b^2 = (2)^2 = 4\)[/tex]
3. Multiply the squared values by their respective coefficients:
- [tex]\(2a^2 = 2 \cdot 36 = 72\)[/tex]
- [tex]\(5b^2 = 5 \cdot 4 = 20\)[/tex]
4. Add the results together:
- [tex]\(2a^2 + 5b^2 = 72 + 20 = 92\)[/tex]
So, the value of the expression [tex]\(2a^2 + 5b^2\)[/tex] when [tex]\(a = -6\)[/tex] and [tex]\(b = 2\)[/tex] is [tex]\(\boxed{92}\)[/tex].
