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x^2 - x - y^2 - y
= x^2 - y^2 - x - y
= ( x - y ) ( x + y ) - ( x + y )
= ( x + y ) ( x - y - 1 )
x^2 - 2xy + y^2 - z^2
= ( x- y ) ^2 - z^2
= ( x - y - z ) ( x - y + z )
a)\(\left(-a+\frac{2}{3}\right)\left(a+\frac{2}{3}\right)=\left(\frac{2}{3}-a\right)\left(\frac{2}{3}+a\right)=\left(\frac{2}{3}\right)^2-a^2=\frac{4}{9}-a^2\)
b)\(\left(x+5\right)\left(x^2-5x+25\right)=x^3+5^3=x^3+125\)
c)\(\left(1-x\right)\left(x^2+x+1\right)=1-x^3\)
d)\(\left(a^2-2a+3\right)\left(a^2+2a+3\right)=\left(a^2+3\right)^2-\left(2a\right)^2=\left(a^2+3\right)^2-4a^2\)
e)\(\left(x+3y\right)\left(9y^2-3xy+x^2\right)=x^3+\left(3y\right)^3=x^3+9y^3\)
f)\(2\left(x-\frac{1}{2}\right)\left(4x^2+2x+1\right)=\left(2x-1\right)\left(4x^2+2x+1\right)=\left(2x\right)^3-1=8x^3-1\)
\(a.=x\)
\(b.=y^3\)
\(c.=3xy\)
\(d.=-\frac{5}{2}a\)
\(e.=3yz\)
\(f.=-3xy\)
\(2x+3y+5z=\frac{x^2+y^2+z^2}{2}+19\)
\(x^2+y^2+z^2+38=4x+6y+10z\)
\(\left(x^2-4x+4\right)+\left(y^2-6y+9\right)+\left(z^2-10z+25\right)=0\)
\(\left(x-2\right)^2+\left(y-3\right)^2+\left(z-5\right)^2=0\)
\(x-2=y-3=z-5=0\)
\(x=2,y=3,z=5\)