Question

Chứng minh các hằng đẳng thức sau

a/(a-b)³=-(b-a)³

b/(-a-b)²=(a+b)²

help me ai FA lm ny tui ko

Answer 1

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

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

Học tốt!

Answer 2

a) \(-\left(b-a\right)^3=-\left(b-a\right).\left(b-a\right)^2\)

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

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

Answer 3

a,(a-b)³=a³-3a²b+3ab²-b³=-(b³-3ab²+3a²b-a³)=-(b-a)³

b,(-a-b)²=(-1)².(a+b)²=(a+b)²

Answer 4

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

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

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

\(\Rightarrow\)\(dpcm\)