Question

chứng minh (a^(2)+b^(2))^(2)-4a^(2)b^(2)=(a+b)^(2)(a-b)^(2)

Answer 1

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

Answer 2

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

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

<=> vế trái = \(\left(a^2+b^2\right)^2-\left(2ab\right)^2\) (HĐT số 3)

<=> ĐPCM