Question

Chứng minh các hằng đẳng thức sau:

a) (a-b)^3=-(b-a)^3

b) (-a-b)^2=(a+b)^2

Answer 1

a) (a-b)^3=-(b-a)^3

\(Taco:-\left(b-a\right)^3\)

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

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

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

\(=\left(a-b\right)\left(a-b\right)\left(a-b\right)=\left(a-b\right)^3\)

Answer 2

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

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

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

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

Answer 3

\(a,\left(a-b\right)^3=-\left(b-a\right)^3\)

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

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

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

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

\(=\left(a-b\right)^3\)

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

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

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

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