Question

C/m THĐT

1) (A+B)² =A²+2AB+B²

2) (A-B)²=A²-2AB+B²

3) A²-B²=(A-B).(A+B)

4) (A+B)³=A³+3A²B+3AB²+B³

5) (A-B)³=A³-3A²B+3AB²-B³

6) A³+B³=(A+B).(A²-AB+B²)

7) A³-B³=(A-B).(A²+AB+B²)

Answer 1

1)   \(\left(A+B\right)^2=\left(A+B\right)\left(A+B\right)=A\left(A+B\right)+B\left(A+B\right)\)

\(=A^2+AB+AB+B^2=A^2+2AB+B^2\)

2)  \(\left(A-B\right)^2=\left(A-B\right)\left(A-B\right)=A\left(A-B\right)-B\left(A-B\right)\)

\(=A^2-AB-AB+B^2=A^2-2AB+B^2\)

3)  \(A^2-B^2=A^2-AB-B^2+AB\)

\(=A\left(A-B\right)+B\left(A-B\right)=\left(A-B\right)\left(A+B\right)\)

p/s: mấy cái kia tương tự