Complete the table
$\begin{matrix} first expression & second expression & product (i) & a & b + c + d & - - - (i i) & x + y - 5 & 5 x y & - - - (i i i) & p & 6 p^{2} - 7 p + 5 & - - - (i v) & 4 p^{2} q^{2} & p^{2} - q^{2} & - - - (v) & a + b + c & a b c & - - - - \end{matrix}$

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Solution

(i) Given, $a \times (b + c + d) = a b + a c + a d$
(ii) Given, $(x + y - 5) \times 5 x y = x (5 x y) + y (5 x y) - 5 (5 x y)$
$= 5 x^{2} y + 5 x y^{2} - 25 x y$
(iii) $p \times (6 p^{2} - 7 p + 5) = p (6 p^{2}) - p (7 p) + p (5)$
$= 6 p^{3} - 7 p^{2} + 5 p$
(iv) Given $4 p^{2} q^{2} (p^{2} - q^{2}) = 4 p^{2} q^{2} (p^{2}) - 4 p^{2} q^{2} (q^{2})$
$4 p^{2 + 2} q^{2} - 4 p^{2} q^{2 + 2}$ (Since, when the bases are same then exponents will be added)
$= 4 p^{4} q^{2} - 4 p^{2} q^{4}$
(v) Given $(a + b + c) \times a b c = a (a b c) + b (a b c) + c (a b c)$
$= a^{2} b c + a b^{2} c + a b c^{2}$
Thus, the table can be completed as follows.
$\begin{matrix} first expression & second expression & product (i) & a & b + c + d & a b + a c + a d (i i) & x + y - 5 & 5 x y & 5 x^{2} y + 5 x y^{2} - 25 x y (i i i) & p & 6 p^{2} - 7 p + 5 & 6 p^{3} - 7 p^{2} + 5 p (i v) & 4 p^{2} q^{2} & p^{2} - q^{2} & 4 p^{4} q^{2} - 4 p^{2} q^{4} (v) & a + b + c & a b c & a^{2} b c + a b^{2} c + a b c^{2} \end{matrix}$

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Similar questions

Q. Complete the table.

First expression	Second expression	Product
(i) $a$	$b + c + d$	.....
(ii) $x + y - 5$	$5 x y$	.....
(iii) $p$	$6 p^{2} - 7 p + 5$	.....
(iv) $4 p^{2} q^{2}$	$p^{2} - q^{2}$	.....
(v) $a + b + c$	$a b c$	.....

	First Expression	Second Expression	Product
i)	$a$	$b + c + d$
ii)	$x + y - 5$	$5 x y$
iii)	$p$	$6 p^{2} - 7 p + 5$
iv)	$4 p^{2} q^{2}$	$p^{2} - q^{2}$
v)	$a + b + c$	$a b c$

complete the table

Question 2
Complete the table:
$\begin{matrix} First expression & Second expression & Product (i) & a & b + c + d & - - (i i) & x + y - 5 & 5 x y & - - (i i i) & p & 6 p^{2} - 7 p + 5 & - - (i v) & 4 p^{2} q^{2} & p^{2} - q^{2} & - - (v) & a + b + c & a b c & - - \end{matrix}$

Q. Complete the table.

	First Expression	Second Expression	Product
I)	$a$	$b + c + d$	.....
II)	$x + y - 5$	$5 x y$	.....
III)	$p$	$6 p^{2} - 7 p + 5$	.....
IV)	$4 p^{2} q^{2}$	$p^{2} - q^{2}$	.....
V)	$a + b + c$	$a b c$	.....

Complete the table of products.

$\begin{matrix} F i r s t P o l y n o m i a l \to & a^{2} + b^{2} & c + 5 d^{2} & - 6 p^{2} + 5 p S e c o n d P o l y n o m i a l ↓ - a b + d - c d + a b a b c d - p q \end{matrix}$
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Complete the tablefirst expression second expression product(i)ab+c+d−−−(ii)x+y−55xy−−−(iii)p6p2−7p+5−−−(iv)4p2q2p2−q2−−−(v)a+b+cabc−−−−

Complete the table
$\begin{matrix} first expression & second expression & product (i) & a & b + c + d & - - - (i i) & x + y - 5 & 5 x y & - - - (i i i) & p & 6 p^{2} - 7 p + 5 & - - - (i v) & 4 p^{2} q^{2} & p^{2} - q^{2} & - - - (v) & a + b + c & a b c & - - - - \end{matrix}$