Question

Express each of the following product as a monomials and verify the result for x = 1, y = 2:
$\left(\frac{2}{5}{a}^{2}b\right)\times \left(-15b^{2}ac\right)\times \left(-\frac{1}{2}{c}^2\right)$

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:

$$\begin{gathered} \left(\frac{2}{5}{a}^{2}b\right)\times \left(-15b^{2}ac\right)\times \left(-\frac{1}{2}{c}^2\right) \\ =\left\{\frac{2}{5}\times \left(-15\right)\times \left(-\frac{1}{2}\right)\right\}\times \left(a^2\times a\right)\times \left(b\times b^2\right)\times \left(c\times c^2\right) \\ =\left\{\frac{2}{5}\times \left(-15\right)\times \left(-\frac{1}{2}\right)\right\}\times \left(a^{2+1}\right)\times \left(b^{1+2}\right)\times \left(c^{1+2}\right) \\ =3a^3{b}^3{c}^3 \end{gathered}$$

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

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

Thus, the answer is $3a^3{b}^3{c}^3$.