Question

Answer 1

\(\left(a^2+ab+b^2\right)\left(a^2-ab+b^2\right)-\left(a^4+b^4\right)\)

\(=\left[\left(a^2+b^2\right)+ab\right]\left[\left(a^2+b^2\right)-ab\right]-\left(a^4+b^4\right)\)

\(=\left(a^2+b^2\right)^2-a^2b^2-a^4-b^4\)

\(=a^4+b^4+2a^2b^2-a^2b^2-a^4-b^4=a^2b^2\)

Answer 2

\(k,=\left(a^2+b^2\right)^2-\left(ab\right)^2-a^4-b^4\\ =a^4+2a^2b^2+b^4-a^2b^2-a^4-b^4\\ =a^2b^2\)