Question

Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)

Answer 1

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:

$$\begin{gathered} \left(3x\right)\times \left(4x\right)\times \left(-5x\right) \\ =\left\{3\times 4\times \left(-5\right)\right\}\times \left(x\times x\times x\right) \\ =\left\{3\times 4\times \left(-5\right)\right\}\times \left(x^{1+1+1}\right) \\ =-60x^3 \end{gathered}$$

Substituting x = 1 in LHS, we get:

$$\begin{gathered} \text{LHS}=\left(3x\right)\times \left(4x\right)\times \left(-5x\right) \\ =\left(3\times 1\right)\times \left(4\times 1\right)\times \left(-5\times 1\right) \\ =-60 \end{gathered}$$

Putting x = 1 in RHS, we get:
$$\begin{gathered} \text{RHS}=-60x^3 \\ =-60{\left(1\right)}^3 \\ =-60\times 1 \\ =-60 \end{gathered}$$


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

Thus, the answer is $-60x^3$.