What is the algebra behind the manipulation of exponents shown here?

Question

$8(8^k) - 3(3^k)$ is the first step, and then it gets manipulated into.

$(8^k - 3^k)8 + 5(3^k)$ this manipulation is correct as they do hold the same values when inputting a value for $k$ but I do not understand how the manipulation occurred?

Thank you.

Answer 1

\begin{align} 8(8^k)-3(3^k)&= 8(8^k)-(8-5)(3^k)\\ &= 8 (8^k)-8(3^k)+5(3^k)\\ &=8(8^k-3^k)+5(3^k) \end{align}

Answer 2

We have $8(8^k)-3(3^k)$, subtracting and adding $5(3^k)$ gives $8(8^k)-8(3^k)+5(3^k) = 8(8^k-3^k)+5(3^k)$.

Q.E.D

Answer 3

$$8(8^k) - 3(3^k)=8(8^k) -(8-5)(3^k) $$

$$8(8^k) - 8(3^k) +5(3^k)=$$

$$8(8^k-3^k) +5(3^k)$$