Question

Express each of the following product as a monomials and verify the result for x = 1, y = 2:
$\left(\frac{4}{9}ab{c}^3\right)\times \left(-\frac{27}{5}{a}^3{b}^2\right)\times \left(-8b^{3}c\right)$

Answer 1

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e.,​ $a^m\times a^n=a^{m+n}$.

We have:

$$\begin{gathered} \left(\frac{4}{9}ab{c}^3\right)\times \left(-\frac{27}{5}{a}^3{b}^2\right)\times \left(-8b^{3}c\right) \\ =\left\{\left(\frac{4}{9}\right)\times \left(-\frac{27}{5}\right)\times \left(-8\right)\right\}\times \left(a\times a^3\right)\times \left(b\times b^2\times b^3\right)\times \left(c^3\times c\right) \\ =\left\{\left(\frac{4}{9}\right)\times \left(-\frac{27}{5}\right)\times \left(-8\right)\right\}\times \left(a^{1+3}\right)\times \left(b^{1+2+3}\right)\times \left(c^{3+1}\right) \\ =\frac{96}{5}{a}^4{b}^6{c}^4 \end{gathered}$$

Thus, the answer is $\frac{96}{5}{a}^4{b}^6{c}^4$.​

$\because$ The expression doesn't consist of the variables x and y.

$\therefore$ The result cannot be verified for x = 1 and y = 2