# Find the product and reduce to lowest terms. \frac{vw - vx + wz - xz}{kv + nv - kz - nz} \times...

## Question:

Find the product and reduce to lowest terms.

{eq}\displaystyle \frac{vw - vx + wz - xz}{kv + nv - kz - nz} \times \frac{vw + vx - wz - xz}{vw + vx + wz + xz} {/eq}

## Algebraic Expressions

We have to multiply and then simplify the given algebraic expression. Very often in such cases, the simplification and the multiplication go together. We have to do both simultaneously.

\begin{align} &\frac{vw - vx + wz - xz}{kv + nv - kz - nz} *\frac{vw + vx - wz - xz}{vw + vx + wz + xz}\\ =&\frac{v(w-x)+z(w-x)}{v(k+n)-z(k+n)} *\frac{v(w+x)-z(w+x)}{v(w+x)+z(w+x)}\\ =&\frac{(v+z)(w-x)}{(v-z)(k+n)} *\frac{(v-z)(w+x)}{(v+z)(w+x)}\\ =&\frac{w-x}{k+n} \end{align}

The required operation can be performed as follows.

\begin{align} &\frac{vw - vx + wz - xz}{kv + nv - kz - nz} *\frac{vw + vx - wz - xz}{vw + vx + wz + xz}\\ =&\frac{v(w-x)+z(w-x)}{v(k+n)-z(k+n)} *\frac{v(w+x)-z(w+x)}{v(w+x)+z(w+x)}\\ =&\frac{(v+z)(w-x)}{(v-z)(k+n)} *\frac{(v-z)(w+x)}{(v+z)(w+x)}\\ =&\frac{w-x}{k+n} \end{align}