Question

(a^2+2b^2)whole square-4a^2b^2

Answer 1

Answer:

a^4+4b^4

Step-by-step explanation:

1. First we try and simplify the expression ((a^2+2b^2))^2 (if i understood this correctly). We do this by rewriting it as (a^2+2b^2)(a^2+2b^2).

2. Expand this using the FOIL method (First,Outer,Inner,Last) and get a^2(a^2+2b^2)+2b^2(a^2+2b^2)

3. Distribute it to simplify easily: a^2a^2+a^2(2b^2)+2b^2a^2+2b^2(2b^2)

4. Simplify completely and you get a^4+4a^2b^2+4b^4

5. Rewrite it clearly with the subtraction part and then, since both terms are perfect squares, factorise using the difference of squares: (a^2+2b^2+2ab)(a^2+2b^2-(2ab))

6. Simplify it further and you get the answer a^4+4b^4