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: 

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

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

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

$$=-60x^3$$

Substituting x = 1 in LHS, we get:

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

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

$$=-60$$

Putting x = 1 in RHS, we get:

$$\text{ RHS }=-60x^3$$

$$=-60{\left(1\right)}^3$$

$$=-60\times 1$$

$$=-60$$

$$\because$$ LHS = RHS for x = 1; therefore, the result is correct
Thus, the answer is $$-60x^3$$.