a ) \(VT=\left(x+y+z\right)^2-\left(x-y-z\right)^2\)
\(=\left(x+y+z-x+y+z\right)\left(x+y+z+x-y-z\right)\)
\(=4x\left(y+z\right)=VP\)
b ) \(VT=\left(2a+b\right)^2-\left(a+b\right)^2-3a^2\)
\(=\left(2a+b-a-b\right)\left(2a+b+a+b\right)-3a^2\)
\(=a\left(3a+2b\right)-3a^2\)
\(=3a^2+2ab-3a^2=2ab=VP\)
a) \(\left(x+y+z\right)^2-\left(x-y-z\right)^2=4x\left(y+z\right)\)
\(\Rightarrow x^2+y^2+z^2+2xy+2xz+2yz-\left(x^2+y^2+z^2-2xy-2xz+2yz\right)=4x\left(y+z\right)\)\(\Rightarrow x^2+y^2+z^2+2xy+2xz+2yz-x^2-y^2-z^2+2xy+2xz-2yz=4x\left(y+z\right)\)\(\Leftrightarrow4xy+4xz=4x\left(y+z\right)\)
\(\Leftrightarrow4x\left(y+z\right)=4x\left(y+z\right)\).
b) \(\left(2a+b\right)^2-\left(a+b\right)^2-3a^2=2ab\)
\(\Rightarrow\left(2a\right)^2+2.2a.b+b^2-\left(a^2+2ab+b^2\right)-3a^2=2ab\)
\(\Rightarrow4a^2+4ab+b^2-a^2-2ab-b^2-3a^2=2ab\)
\(\Leftrightarrow2ab=2ab\)
