Find the product $(a^{2} + b) (a + b^{2})$

a^{3} + b^{3} + 2 a b (a b - 1)

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a^{2} + b^{2} + 2 a b - 3 b^{2}

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a^{2} + b^{2} + a b (a b + b^{2})

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a^{3} + b^{3} + a b (a b + 1)

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Solution

The correct option is D $a^{3} + b^{3} + a b (a b + 1)$
$(a^{2} + b) (a + b^{2})$
$= a^{2} (a + b^{2}) + b (a + b^{2})$
$= a^{3} + a^{2} b^{2} + a b + b^{3}$
$= a^{3} + b^{3} + a b (a b + 1)$

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Similar questions

Q. Expand

a^{3} b^{2}, a^{2} b^{3}, b^{2} a^{3}, b^{3} a^{2} .

Are they all same?

Q. Which of the following equations are correct?

(i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a)

(i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)

(i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)

(i v) a^{2} - b^{2} = (a + b) (a - b)

Which of the following equation/s is/are correct?

$i) (a + b + c)^{2} = a^{2} + b^{2} + c^{2} - 2 (a b + b c + c a)$
$i i) (a + b)^{3} = a^{3} + b^{3} + 3 a b (a - b)$
$i i i) (a - b)^{3} = a^{3} - b^{3} - 3 a b (a + b)$
$i v) a^{2} - b^{2} = (a + b) (a - b)$