Simplifying exponents (How does $(2^6 + 2^3)(2^6-2^3)$ get created from $(2^6)^2 - (2^3)^2$

Question

How does $(2^6 + 2^3)(2^6-2^3)$ get created from $(2^6)^2 - (2^3)^2$? Can someone explain?

Answer 1

By the difference of perfect squares. $$\large(a+b)(a-b) = (a+b)a - (a+b)b = a^2+ab-ab-b^2=a^2-b^2$$ We just have to let $a = 2^6$ and $b=2^3$.

Answer 2

There is a rule from algebra that $(a+b)(a-b)=a^2-b^2$ (because the middle terms have opposite sign and cancel). In your case, using $a=2^6$ and b=$2^3$ you can fill in the missing step of factoring the numerator to get a like term with the denominator.