Question

Chứng minh rằng:
a) \(\left(a+b\right)^2=a^2+2ab+b^2\)

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

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

Answer 1

\(a,b)\)Ta có: \(\left(a\pm b\right)^2\)

\(=\left(a\pm b\right)\left(a\pm b\right)\)

\(=a^2\pm ab\pm ab+b^2\)

\(=a^2\pm ab+b^2\)

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

Answer 2

a.) \(\left(a+b\right)^2=\left(a+b\right).\left(a+b\right)=a^2+ab+ba+b^2=a^2+2ab+b^2\)

b.) \(\left(a-b\right)^2=\left(a-b\right).\left(a-b\right)=a^2-ab-ba+b^2=a^2-2ab+b^2\)

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