## Answer

$\frac{a^{3}}{3}-100a+C_0$

## Step-by-step explanation

Problem to solve:

$\int\left(a-10\right)\left(a+10\right)da$

1

The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: $(a+b)(a-b)=a^2-b^2$, where:

- The first term ($a$) is $a$.
- The second term ($b$) is $10$.

$\int\left(a^2-100\right)da$

2

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int a^2da+\int-100da$

## Answer

$\frac{a^{3}}{3}-100a+C_0$