Simplify each of the following products:$ (m+\frac{n}{7})^{3}(m-\frac{n}{7}) $

Given:

\( (m+\frac{n}{7})^{3}(m-\frac{n}{7}) \)

To do:

We have to simplify the given product.

Solution:

We know that,

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

$(a+b)(a-b)=a^2-b^2$

Therefore,

$(m+\frac{n}{7})^{3}(m-\frac{n}{7})=(m+\frac{n}{7})^{2}(m+\frac{n}{7})(m-\frac{n}{7})$

$=(m+\frac{n}{7})^{2}(m^{2}-(\frac{n}{7})^{2})$

$=(m+\frac{n}{7})^{2}(m^{2}-\frac{n^{2}}{49})$

Hence, $(m+\frac{n}{7})^{3}(m-\frac{n}{7})=(m+\frac{n}{7})^{2}(m^{2}-\frac{n^{2}}{49})$.

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Updated on: 10-Oct-2022

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