# Ex.9.2 Q1 Algebraic Expressions and Identities - NCERT Maths Class 8

## Question

Find the product of the following pairs of monomials.

(i) \(\quad 4,7p\)

(ii)\(\quad -\text{ }4p,\text{ }7p~\)

(iii)\(\quad - 4p,\;7pq\)

(iv)\(\quad 4{p^3},\; - {\rm{ }}3p\)

(v)\(\quad 4p,\;0\)

## Text Solution

**What is known?**

Pairs of monomials

**What is unknown?**

Product

**Reasoning:**

i) By using the distributive law, we can carry out the multiplication term by term.

ii) In multiplication of polynomials with polynomials, we should always look for like terms, if any, and combine them.

**Steps:**

The product will be as follows.

(i)

\[\begin{align} &4 \times 7p\\ &= 4 \times 7 \times p \\&= 28p \end{align}\]

(ii)

\[\begin{align} & - 4p \times 7p \\&=- 4 \times p \times 7 \times p \\&= \left( { - 4 \times 7} \right) \times \left( {p \times p} \right) \\&=- 28{p^2} \end{align}\]

(iii)

\[\begin{align} & - 4p \times 7pq \\&=- 4 \times p \times 7 \times p \times q \\&= \left( { - 4 \times 7} \right) \times \left( {p \times p \times q} \right) \\& =- 28{p^2}q \end{align}\]

(iv)

\[\begin{align} & 4{p^3} \times- 3p \\&= 4 \times \left( { - 3} \right) \times p \times p \times p \times p \\&=- 12{p^4} \end{align}\]

(v)

\[\begin{align} & 4p \times 0 \\&= 4 \times p \times 0 \\&= 0 \end{align}\]