To evaluate the expression [tex]\( 8a^2 - 6a \)[/tex] when [tex]\( a = \frac{1}{2} \)[/tex], follow these steps:
1. Substitute [tex]\( a = \frac{1}{2} \)[/tex] into the expression:
[tex]\[
8 \left( \frac{1}{2} \right)^2 - 6 \left( \frac{1}{2} \right)
\][/tex]
2. Calculate [tex]\( \left( \frac{1}{2} \right)^2 \)[/tex]:
[tex]\[
\left( \frac{1}{2} \right)^2 = \frac{1}{4}
\][/tex]
3. Multiply by 8:
[tex]\[
8 \times \frac{1}{4} = 2
\][/tex]
4. Calculate [tex]\( 6 \times \frac{1}{2} \)[/tex]:
[tex]\[
6 \times \frac{1}{2} = 3
\][/tex]
5. Substitute these values back into the expression:
[tex]\[
2 - 3
\][/tex]
6. Perform the subtraction:
[tex]\[
2 - 3 = -1
\][/tex]
So, when [tex]\( a = \frac{1}{2} \)[/tex], the value of the expression [tex]\( 8a^2 - 6a \)[/tex] is [tex]\(-1\)[/tex].
