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

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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?


What is unknown?



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.



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


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


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


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


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

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