Complete the operation. \frac{36x^2 - 49y^2}{6x + 7y}

Question:

Complete the operation.

{eq}\frac{36x^2 - 49y^2}{6x + 7y} {/eq}

Factorisation

Consider for the expression,

{eq}a^2\ -\ b^2 {/eq},

using the factorisation, we can write it as

{eq}\displaystyle a^2\ -\ b^2\ =\ a^2\ -\ ab\ -\ b^2\ +\ ab\ =\ a(a\ -\ b)\ +\ b(-b\ +\ a)\ =\ (a\ +\ b)\ \times\ (a\ -\ b) {/eq}

So the final relation, we come across is,

{eq}\displaystyle (a^2\ -\ b^2)\ =\ (a\ -\ b)(a\ +\ b) {/eq}

Answer and Explanation:

Here, we have

{eq}\displaystyle \frac{36x^2 - 49y^2}{6x + 7y} {/eq}

Now, using the above mentioned relation,

{eq}\displaystyle 36x^2\ -\ 49y^2\ =\ (6x)^2\ -\ (7y)^2\ =\ (6x\ -\ 7y)(6x\ +\ 7y) {/eq}

Now after putting in the original relation, we get

{eq}\displaystyle \frac{36x^2 - 49y^2}{6x + 7y} \ =\ \frac{(6x\ -\ 7y)(6x\ +\ 7y)}{6x + 7y}\ =\ 6x\ -\ 7y {/eq}


Learn more about this topic:

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Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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