Question

Pls help me simplify thisss

Answer 1

9514 1404 393

Answer:

  2a(a^3 +a^3 b^2 +a b^2 +b^3)/(a^2 +b^2)

Step-by-step explanation:

Division is the same as multiplication by the inverse. Multiplication and division proceed left-to-right. So, we can rewrite the expression as ...

  $\dfrac{a^3+a^3b^2+ab^2+b^3}{2a(a-b)^2}\times\dfrac{a^2-b^2}{a+2b}\times\dfrac{a^2+ab-2b^2}{a+b}\times\dfrac{4a^2}{a^2+b^2}\\\\=\dfrac{(a^3+a^3b^2+ab^2+b^3)(a-b)(a+b)(a+2b)(a-b)(4a^2)}{2a(a-b)^2(a+2b)(a+b)(a^2+b^2)}\\\\=\dfrac{4a^2}{2a}\cdot\dfrac{(a-b)^2}{(a-b)^2}\cdot\dfrac{a+2b}{a+2b}\cdot\dfrac{a^3+a^3b^2+ab^2+b^3}{a^2+b^2}\\\\=\boxed{\dfrac{2a(a^3+a^3b^2+ab^2+b^3)}{a^2+b^2}}$