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Simplify $(x-y+z)(x+y-z)-(x+y+z)(x-y-z)$
*hint: expanding everything would take a long time. Can you substitute two variables with one variable?

Simplify $(a-b-c+d)(a+b-c-d)$
*hint: expanding everything would take a long time. Can you substitute two variables with one variable?

If $a+b=2$ and $ab=-1$, evaluate $(a^2-1)(b^2-1)$.

If $\frac{y}{x}+\frac{x}{y}=3$, evaluate $\frac{2x^2-3xy+2y^2}{x^2+y^2}$.

Evaluate $\frac{2003^2-2001\times2003-2}{2}$ without using a calculator.

If $5x=4y$, evaluate $\frac{x^2+xy+y^2}{x^2-xy+y^2}$.

*Give your answer as an improper fraction in simplest terms.

If $a+b=5$, $c+d=2$ and $ad=bc=1$, evaluate:
a) $ac+bd$
b) $\frac{a}{c}$. Give your answer as an improper fraction in simplest terms.