Multiply $(7 x^{2} y + 2 x + 3)$ by $(2 x + 3 y) .$

21 x^{3} y + 14 x^{2} y^{2} + 2 x^{2} + 6 x y + 6 x + 9 y

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14 x^{3} y + 21 x^{2} y^{2} + 4 x^{2} + 6 x y + 6 x + 9 y

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7 x^{3} y + 14 x^{2} y^{2} + 14 x^{2} + 6 x y + 6 x + 9 y

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14 x^{3} y + 21 x^{2} y^{2} + 4 x^{2} + 9 x y + 9 x + 6 y

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Solution

The correct option is B $14 x^{3} y + 21 x^{2} y^{2} + 4 x^{2} + 6 x y + 6 x + 9 y$
$= (7 x^{2} y + 2 x + 3) \times (2 x + 3 y)$
$= 2 x (7 x^{2} y + 2 x + 3) + 3 y (7 x^{2} y + 2 x + 3)$
$= 14 x^{3} y + 4 x^{2} + 6 x + 21 x^{2} y^{2} + 6 x y + 9 y$
$= 14 x^{3} y + 21 x^{2} y^{2} + 4 x^{2} + 6 x y + 6 x + 9 y$

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First monomial $\to$ Second Monomial $↓$	$2 x$	$- 3 y$	$4 x^{2}$	$- 5 x y$	$7 x^{2} y$	$- 6 x^{2} y^{2}$
$2 x$	$4 x^{2}$	....	....
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$F i r s t m o n o m i a l \to - --------------- \to ↓ S e c o n d m o n o m i a l$	2x	-5y	$3 x^{2}$	-4xy	$7 x^{2} y$	$- 9 x^{2} y^{2}$
2x	$4 x^{2}$	-	-	-	-	-
- 5y	-	-	$- 15 x^{2} y$	-	-	-
$3 x^{2}$	-	-	-	-	-	-
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$7 x^{2} y$	-	-	-	-	-	-
$- 9 x^{2} y^{2}$	-	-	-	-	-	-

$\frac{F i r s t m o n o m i a l \to}{S e c o n d m o n o m i a l ↓}$	$2 x$	$- 5 y$	$3 x^{2}$	$- 4 x y$	$7 x^{2} y$	$- 9 x^{2} y^{2}$
$2 x$	$4 x^{2}$	.....	.....	.....	.....	.....
$- 5 y$	.....	.....	$- 15 x^{2} y$	.....	.....	.....
$3 x^{2}$	.....	.....	.....	.....	.....	.....
$- 4 x y$	.....	.....	.....	.....	.....	.....
$7 x^{2} y$	.....	.....	.....	.....	.....	.....
$- 9 x^{2} y^{2}$	.....	.....	.....	.....	.....	.....

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