Express each of the following products as a monomial and verify the result in each case for $x = 1$:
$ \left(4 x^{2}\right) \times(-3 x) \times\left(\frac{4}{5} x^{3}\right) $

Given:

\( \left(4 x^{2}\right) \times(-3 x) \times\left(\frac{4}{5} x^{3}\right) \)

To do:

We have to express the given product as a monomial and verify the result for $x = 1$:

Solution:

$(4 x^{2}) \times(-3 x) \times(\frac{4}{5} x^{3})=4 \times(-3) \times \frac{4}{5} \times x^{2} \times x \times x^{3}$

$=\frac{-48}{5} x^{2+1+3}$

$=\frac{-48}{5} x^{6}$

LHS $=(4 x^{2}) \times(-3 x) \times(\frac{4}{5} x^{3})$

$=(4 \times 1^{2}) \times(-3 \times 1) \times(\frac{4}{5} \times 1^{3})$

$=4 \times 1 \times(-3 \times 1) \times \frac{4}{5} \times 1$

$=\frac{-48}{5}$

RHS $=\frac{-48}{5}(x^{6})$

$=\frac{-48}{5}(1)^{6}$

$=\frac{-48}{5} \times 1$

$=\frac{-48}{5}$

Therefore,

LHS $=$ RHS

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Updated on: 10-Oct-2022

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