Question

rút gọn biểu thức

a. \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)

b. \(\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2\)

 

Answer 1

a.\(=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2+2ab-2bc-2ac-2\left(a^2+2ab+b^2\right)=2a^2+2b^2+2c^2+4ab-2a^2-2ab-2b^2=2c^2+2ab\)

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