Question

Express each of the following product as a monomials and verify the result for x = 1, y = 2:

\[\left( \frac{2}{5} a^2 b \right) \times \left( - 15 b^2 ac \right) \times \left( - \frac{1}{2} c^2 \right)\]

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:

\[\left( \frac{2}{5} a^2 b \right) \times \left( - 15 b^2 ac \right) \times \left( - \frac{1}{2} c^2 \right)\]

\[ = \left\{ \frac{2}{5} \times \left( - 15 \right) \times \left( - \frac{1}{2} \right) \right\} \times \left( a^2 \times a \right) \times \left( b \times b^2 \right) \times \left( c \times c^2 \right)\]

\[ = \left\{ \frac{2}{5} \times \left( - 15 \right) \times \left( - \frac{1}{2} \right) \right\} \times \left( a^{2 + 1} \right) \times \left( b^{1 + 2} \right) \times \left( c^{1 + 2} \right)\]

\[ = 3 a^3 b^3 c^3\]

\[\because\] 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 \[3 a^3 b^3 c^3\].