Question

Rút gọn

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

b,\(\left(a+2b\right)^2+\left(b-a\right)^2-\left(a-b\right)^2\)

2.CMR. \(\left(a-b\right)^2=\left(b-a\right)^2\)

3.Tính \(\left(a-b\right)^4\)

Answer 1

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

\(=-2b\left(2a\right)=-4ab\)

b) ta có : \(\left(a+2b\right)^2+\left(b-a\right)^2-\left(a-b\right)^2=\left(a+2b\right)^2+\left(b-a\right)-\left(b-a\right)^2\)

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

2) ta có : \(\left(a-b\right)^2=\left(-\left(b-a\right)\right)^2=\left(b-a\right)^2\left(đpcm\right)\)

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

\(=a^4-2a^3b+a^2b^2-2a^3b+4a^2b^2-2ab^3+b^2a^2-2ab^3+b^4\)

\(=a^4-4a^3b+6a^2b^2-4ab^3+b^4\)