Question

Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x²) × (−3x) × $\left(\frac{4}{5}{x}^3\right)$

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:

$$\begin{gathered} \left(4x^2\right)\times \left(-3x\right)\times \left(\frac{4}{5}{x}^3\right) \\ =\left\{4\times \left(-3\right)\times \frac{4}{5}\right\}\times \left(x^2\times x\times x^3\right) \\ =\left\{4\times \left(-3\right)\times \frac{4}{5}\right\}\times \left(x^{2+1+3}\right) \\ =-\frac{48}{5}{x}^6 \end{gathered}$$

$\therefore$ $\left(4x^2\right)\times \left(-3x\right)\times \left(\frac{4}{5}{x}^3\right)=-\frac{48}{5}{x}^6$

Substituting x = 1 in LHS, we get:

$$\begin{gathered} \text{LHS}=\left(4x^2\right)\times \left(-3x\right)\times \left(\frac{4}{5}{x}^3\right) \\ =\left(4\times 1^2\right)\times \left(-3\times 1\right)\times \left(\frac{4}{5}\times 1^3\right) \\ =4\times \left(-3\right)\times \frac{4}{5} \\ =-\frac{48}{5} \end{gathered}$$

Putting x = 1 in RHS, we get:

$$\begin{gathered} \text{RHS}=-\frac{48}{5}{x}^6 \\ =-\frac{48}{5}\times 1^6 \\ =-\frac{48}{5} \end{gathered}$$

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

Thus, the answer is $-\frac{48}{5}{x}^6$.