Question

a/ \(\left(x+y\right)^2-y^2=x\left(x+2y\right)\)

b/ \(\left(x^2+y^2\right)^2-\left(2xy\right)^2=\left(x+y\right)^2\left(x-y\right)^2\)

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

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

Answer 1

a) \(\left(x+y\right)^2-y^2=x\left(x+y^2\right)\)

\(\Leftrightarrow\left(x+y+y\right)\left(x+y-y\right)=x^2+xy^2\)

\(\Leftrightarrow\left(x+2y\right)x=x^2+xy^2\)

\(\Leftrightarrow x^2+2xy-x^2-xy=0\)

\(\Leftrightarrow xy=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\y=0\\x=y=0\end{matrix}\right.\)

Answer 2

a) Ta có:

\(VT=\left(x+y\right)^2-y^2\)

\(VT=x^2+2xy+y^2-y^2\)

\(VT=x^2+2xy\) (1)

\(VP=x\left(x+2y\right)\)

\(VP=x^2+2xy\) (2)

Từ (1) và (2) \(\Rightarrow VT=VP\) \(\RightarrowĐPCM\)