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

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:

$(3 x) \times(4 x) \times(-5 x)$

$=\{3 \times 4 \times(-5)\} \times(x \times x \times x)$

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

$=-60 x^{3}$

Substituting x = 1 in LHS, we get:

LHS $=(3 x) \times(4 x) \times(-5 x)$

$=(3 \times 1) \times(4 \times 1) \times(-5 \times 1)$

$=-60$

Putting x = 1 in RHS, we get:

RHS $=-60 x^{3}$

$=-60(1)^{3}$

$=-60 \times 1$

$=-60$

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

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