# Ex.9.3 Q1 Algebraic Expressions and Identities - NCERT Maths Class 8

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## Question

Carry out the multiplication of the expressions in each of the following pairs.

(i) $$\quad 4p,\,q + r$$

(ii)$$\quad ab,\,a - b$$

(iii)$$\quad a + b,\,7{a^2}{b^2}$$

(iv)$$\quad {a^2} - 9,\,4a$$

(v)$$\quad pq + qr + rp,\,0$$

## Text Solution

What is known?

Expressions

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:

(i)

\begin{align} &\left( {4p} \right) \times \left( {q + r} \right) \\ &= \left( {4p \times q} \right) + \left( {4p \times r} \right) \\& = 4pq + 4pr\end{align}

(ii)

\begin{align} & \left( {ab} \right) \times \left( {a - b} \right) \\ &= \left( {ab \times a} \right) + \left[ {ab \times \left( { - b} \right)} \right] \\ &= {a^2}b - a{b^2}\end{align}

(iii)

\begin{align} & \left( {a + b} \right) \times \left( {7{a^2}{b^2}} \right) \\ &= \left( {a \times 7{a^2}{b^2}} \right) + \left( {b \times 7{a^2}{b^2}} \right) \\ &= 7{a^3}{b^2} + 7{a^2}{b^3}\end{align}

(iv)

\begin{align}& \left( {{a^2} - 9} \right) \times \left( {4a} \right) \\ &= \left( {{a^2} \times 4a} \right) + \left[ {\left( { - 9} \right) \times \left( {4a} \right)} \right] \\ &= 4{a^3} - 36a \end{align}

(v)

\begin{align}& \left( {pq + qr + rp} \right) \times 0 \\ &= \left( {pq \times 0} \right) + \left( {qr \times 0} \right) + \left( {rp \times 0} \right) \\ &= 0\end{align}

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