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# Carry out the multiplication of the expressions in each of the following pairs.i) $4p$ , $q + r$ ii) $ab$ , $a - b$ iii) $a + b$ , $7{a^2}{b^2}$ iv) $a{}^2 - 9$ , $4a$ v) $pq + qr + rp$ , $0$

Last updated date: 20th Jun 2024
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Hint: Here we have to find the multiplication of the given expressions.
We have to make a product of the two expressions. Each expression is a combination of variables and constants. First, we have to expand the expression. The next step is to multiply the coefficient and variables to get the desired result.

(i) $4p$ , $q + r$
Let us product the two expressions and expand it
$\Rightarrow 4p \times (q + r)$
Multiplying coefficient and variables we get
$\Rightarrow (4p \times q) + (4p \times r)$
Grouping the bracket terms we get,
$\Rightarrow 4pq + pr$

$\therefore$The multiplication of $4p$ , $q + r$ is $4pq + pr$.

(ii) $ab$ , $a - b$
Let us product the two expressions and expand it
$\Rightarrow \;ab \times (a - b)$
Multiplying coefficient and variables we get,
$\Rightarrow (ab \times a) - (ab \times b)$
Taking the odd variable on the bracket term we get
$\Rightarrow (a \times a)b - a(b \times b)$
Grouping the terms
$\Rightarrow {a^2}b - a{b^2}$

$\therefore$The multiplication of $ab$, $a - b$ is ${a^2}b - a{b^2}$.

(iii) $a + b$ , $7{a^2}{b^2}$
Let us product the two expressions and expand it
$\Rightarrow (a + b) \times 7{a^2}{b^2}$
Multiplying coefficient and variables we get,
$\Rightarrow (a \times 7{a^2}{b^2}) + (b \times 7{a^2}{b^2})$
Grouping the terms
$\Rightarrow 7{a^3}{b^2} + 7{a^2}{b^3}$

$\therefore$ The multiplication of $a + b$ , $7{a^2}{b^2}$ is$7{a^3}{b^2} + 7{a^2}{b^3}$.

(iv) $a{}^2 - 9$ , $4a$
Let product the two expressions and expand it
$\Rightarrow ({a^2} - 9) \times 4a$
Multiplying coefficient and variables we get,
$\Rightarrow ({a^2} \times 4a) - (9 \times 4a)$
Grouping the terms
$\Rightarrow 4{a^3} - 36a$

$\therefore$The multiplication of $a{}^2 - 9$ , $4a$ is $4{a^3} - 36a$.

(v) $pq + qr + rp$ , $0$
Let product the two expressions and expand it
$\Rightarrow (pq + qr + rp) \times 0$
Multiplying coefficient and variables we get,
$\Rightarrow (pq \times 0) + (qr \times 0) + (rp \times 0)$
Since multiplying any term by zero always results in zero as an answer.
Grouping the terms
$\Rightarrow 0 + 0 + 0$
$\Rightarrow 0$

$\therefore$ The multiplication of $pq + qr + rp$, $0$ is $0$.

Note:
Expressions are formed from the variables and the constants. A variable can take any value. The value of expression changes with the value chosen for variables it contains.
Expressions containing one, two, or three terms are called monomial, binomial, trinomial respectively.