Evaluate
\[ (a^2b – b^2a)^2 \]
Solution:
Using identity:
\[ (a-b)^2 = a^2 – 2ab + b^2 \]
\[ (a^2b – b^2a)^2 \]
\[ = (a^2b)^2 – 2(a^2b)(b^2a) + (b^2a)^2 \]
\[ = a^4b^2 – 2a^3b^3 + a^2b^4 \]
\[ (a^2b – b^2a)^2 \]
Using identity:
\[ (a-b)^2 = a^2 – 2ab + b^2 \]
\[ (a^2b – b^2a)^2 \]
\[ = (a^2b)^2 – 2(a^2b)(b^2a) + (b^2a)^2 \]
\[ = a^4b^2 – 2a^3b^3 + a^2b^4 \]