Why do I get two times the base if it's squared when I multiply the value by four?

Question

For example, if I multiply the value of a base squared by four, I also get twice the base if it's squared. Look:$$6^2\cdot4=12^2$$ because $$36\cdot4=144$$and $36$ is the square of $6$ and $144$ is the square of $12$. Why does this always happen?

Answer 1

Because $4 = 2\cdot 2$ and multiplication works like this: $$ 6^2 \cdot 4 = 6\cdot 6 \cdot 4 = 6\cdot 6 \cdot 2\cdot 2 = 6\cdot 2\cdot 6\cdot 2 = (6\cdot 2)^2$$

Answer 2

Suppose that you have $a^2$, then:

$$4 \cdot a^2 = 2^2 \cdot a^2= (2 \cdot a)^2=(2a)^2$$