Question

Chứng minh đẳng thức sau:

(-a - b)² = (a + b)²

Answer 1

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

\(=a^2+2ab+b^2\)(1)

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

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

Answer 2

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

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

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

      Từ \(\left(1\right)\)và \(\left(2\right)\)ta có :

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