evaluate the expression. $\frac{-b^{2}+25a^{2}+5}{3}$ for $a = \frac{1}{5}$ and $b=-12$

Explanation:

Step1: Substitute values of a and b

Substitute $a = \frac{1}{5}$ and $b=- 12$ into $-b^{2}+25a^{2}+5$. [ \begin{align*} &-(-12)^{2}+25\times(\frac{1}{5})^{2}+5\ \end{align*} ]

Step2: Calculate the squares

Calculate $(-12)^{2}=144$ and $(\frac{1}{5})^{2}=\frac{1}{25}$. [ \begin{align*} &-144 + 25\times\frac{1}{25}+5\ \end{align*} ]

Step3: Multiply and simplify

$25\times\frac{1}{25}=1$. Then we have $-144 + 1+5$. [ \begin{align*} &-144+1 + 5\ &=-144+(1 + 5)\ &=-144 + 6\ &=-138 \end{align*} ]

Answer:

$-138$