Rewrite the expression in simplest terms.
$7 x^{3} - 22 x^{2} - 14 x + 5 + (3 x + 4) \times x^{2}$

10 x^{3} - 18 x^{2} - 14 x + 5

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10 x^{3} + 18 x^{2} - 14 x + 5

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10 x^{3} - 18 x^{2} + 14 x + 5

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10 x^{3} - 18 x^{2} - 14 x - 5

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Solution

The correct option is A $10 x^{3} - 18 x^{2} - 14 x + 5$
We need to simplify the expression $7 x^{3} - 22 x^{2} - 14 x + 5$
$+ (3 x + 4) \times x^{2}$

$S t e p 1 : - ------ -$

First, let's simplify the bracket:
$7 x^{3} - 22 x^{2} - 14 x + 5$
$+ (3 x + 4) \times x^{2}$
$= 7 x^{3} - 22 x^{2} - 14 x + 5$
$+ (3 x \times x^{2} + 4 \times x^{2})$
$= 7 x^{3} - 22 x^{2} - 14 x + 5$
$+ (3 x^{2 + 1} + 4 x^{2})$
$= 7 x^{3} - 22 x^{2} - 14 x + 5$
$+ (3 x^{3} + 4 x^{2})$

$S t e p 2 : - ------ -$

Now, combine the like terms together:
$= 7 x^{3} - 22 x^{2} - 14 x + 5$
$+ (3 x^{3} + 4 x^{2})$
$= (7 x^{3} + 3 x^{3}) + (- 22 x^{2} + 4 x^{2})$
$- 14 x + 5$
$= (7 x^{3} + 3 x^{3}) - ----------- - + (- 22 x^{2} + 4 x^{2}) - -------------- -$
$- 14 x + 5$
$= 10 x^{3} - 18 x^{2} - 14 x + 5$

The expression $7 x^{3} - 22 x^{2} - 14 x + 5$
$+ (3 x + 4) \times x^{2}$ when simplified can be written as $10 x^{3} - 18 x^{2} - 14 x + 5$ .

Therefore, option (a.) is the correct answer.

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