Work out the value of the expressiona) 2(m 2+3) when m=−4      ________________________    (1)b) 5(n 3 +10) when  n=-2

a) Calculate the Expression $2(m^2 + 3)$

1. Break Down the Problem

   • Substitute $m = -4$ into the expression $2(m^2 + 3)$.

2. Relevant Concepts

   • We will calculate $m^2$ first, then add 3, and finally multiply the result by 2.

3. Analysis and Detail

   • Calculate $m^2$: $m^2 = (-4)^2 = 16$
   • Now, add 3: $m^2 + 3 = 16 + 3 = 19$
   • Multiply the result by 2: $2(m^2 + 3) = 2 \times 19 = 38$

4. Verify and Summarize

   • Each calculation step follows logically, and the operations have been correctly applied.

Final Answer

The value of the expression $2(m^2 + 3)$ when $m = -4$ is $38$.

b) Calculate the Expression $5(n^3 + 10)$

1. Break Down the Problem

   • Substitute $n = -2$ into the expression $5(n^3 + 10)$.

2. Relevant Concepts

   • First, calculate $n^3$ and then add 10, followed by multiplying the result by 5.

3. Analysis and Detail

   • Calculate $n^3$: $n^3 = (-2)^3 = -8$
   • Now, add 10: $n^3 + 10 = -8 + 10 = 2$
   • Multiply the result by 5: $5(n^3 + 10) = 5 \times 2 = 10$

4. Verify and Summarize

   • The calculations have been verified and all steps are correctly executed.

Final Answer

The value of the expression $5(n^3 + 10)$ when $n = -2$ is $10$.