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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.

Answer and Explanation:

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


The required operation can be performed as follows.


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


Learn more about this topic:

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Solving Word Problems with Algebraic Multiplication Expressions

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