multiplying polynomials-conceptual problem

[jen23]

{[a^(3)-b^(3)]÷[a^(2)-b^(2)]}{[a^(2)+2ab+b^(2)]÷[a^(2)+ab+b^(2)]}={[a-b][a^(2)+ab+b^(2)][a+b][a+b]}÷{[a-b][a^(2)+ab+b^(2)][1]}

why does this factor this way?

I understand how they multiply them together but I get stuck on how they are factoring it to break it down and simplify it because I am expected to use the same concept later in the book with different signs.
thank you!

 

[lookagain]

\(\displaystyle \frac{a^3 - b^3}{a^2 - b^2} \cdot \frac{a^2 + 2ab + b^2}{a^2 + ab + b^2} = \frac{(a - b)(a^2 + ab + b^2)(a + b)(a + b)}{(a - b)(a^2 + ab + b^2)}\)

why does this factor this way?

I understand how they multiply them together but I get stuck on how they are factoring it to break it down and simplify it because I am expected to use the same concept later in the book with different signs.
thank you!

You're missing a factor. There must be a factor of \(\displaystyle \ \ (a + b) \ \\) in the denominator of the right-hand side
of the equation.

You need to look up examples of/formulas for a difference of two squares, a difference of two cubes,
and a perfect square trinomial.

 

[Denis]

What are you asking?
Like, you don't understand why: a^3 - b^3 = (a - b)(a^2 + ab + b^2) ?