Express each of the following product as a monomials and verify the result in each case for x = 1:

(3x) × (4x) × (−5x)

#### Solution

We have to find the product of the expression in order to express it as a monomial.

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

We have:

\[\left( 3x \right) \times \left( 4x \right) \times \left( - 5x \right)\]

\[ = \left\{ 3 \times 4 \times \left( - 5 \right) \right\} \times \left( x \times x \times x \right)\]

\[ = \left\{ 3 \times 4 \times \left( - 5 \right) \right\} \times \left( x^{1 + 1 + 1} \right)\]

\[ = - 60 x^3\]

Substituting x = 1 in LHS, we get:

\[LHS = \left( 3x \right) \times \left( 4x \right) \times \left( - 5x \right)\]

\[ = \left( 3 \times 1 \right) \times \left( 4 \times 1 \right) \times \left( - 5 \times 1 \right)\]

\[ = - 60\]

Putting *x *= 1 in RHS, we get:

\[\text { RHS } = - 60 x^3 \]

\[ = - 60 \left( 1 \right)^3 \]

\[ = - 60 \times 1\]

\[ = - 60\]

\[\because\] LHS = RHS for x = 1; therefore, the result is correct

Thus, the answer is \[- 60 x^3\].