# Express Each of the Following Product as a Monomials and Verify the Result for X = 1, Y = 2: ( 2 5 a 2 B ) × ( − 15 B 2 a C ) × ( − 1 2 C 2 ) - Mathematics

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

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

#### Solution

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 $3 a^3 b^3 c^3$.
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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.3 | Q 29 | Page 14