Prove that:

$(x+y)(x-y)+(y-z)(y-z)+(z+x)(z-x)=0$

Find the following products:

$(x+3)(x-4)$

Find the following products:

$(x-7)(x-5)$

Find the following products:

$(4x+7)(4x-3)$

Find the following products:

$\left(\frac{3}{4}y-2\right)\left(\frac{3}{4}y+4\right)$

Find the following products:

$\left(x+\frac{2}{5}\right)\left(x+\frac{5}{2}\right)$

Find the following products:

$(7x^2-6xy)(7x^2-3xy)$

Find the following products:

$\left(l^2-\frac{1}{2}\right)\left(l^2+\frac{3}{4}\right)$

Evaluate the following using the identity $(x+a)(x+b)=x^2+(a+b)x+ab$.

$103\times 105$