Factorize: $a^{3} + b^{3} + a + b$

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

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

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

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

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Solution

The correct option is B $(a + b) (a^{2} - a b + b^{2} + 1)$
Given, $a^{3} + b^{3} + a + b$

$= (a + b) (a^{2} - a b + b^{2}) + (a + b)$

$= (a + b) (a^{2} - a b + b^{2} + 1)$

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Similar questions

Q. Expand

a^{3} - b^{3}

Question 84 (ix)

Simplify

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

Question 84 (ix)

Simplify

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

Q. If

x = 1 + a + a^{2} + a^{3} + . . . .

\infty (| a | < 1)

and

y = 1 + b + b^{2} + b^{3} + . . .

\infty (| b | < 1)

then

1 + a b + a^{2} b^{2} + a^{3} b^{3} + . . .

\infty = \frac{x y}{x + y - 1}

If x = 1 + a + $a^{2}$ .......... to $\infty$ (|a|<1), y = 1 + b + $b^{2}$ ......... to $\infty$ (|b| < 1), then Z = 1 + ab + $a^{2}$ $b^{2}$ + $a^{3}$ $b^{3}$ ..... to ∞ is

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Factorize: a3+b3+a+b

The correct option is B (a+b)(a2−ab+b2+1)Given, a3+b3+a+b=(a+b)(a2−ab+b2)+(a+b)=(a+b)(a2−ab+b2+1)

Factorize: $a^{3} + b^{3} + a + b$

The correct option is B $(a + b) (a^{2} - a b + b^{2} + 1)$
Given, $a^{3} + b^{3} + a + b$

$= (a + b) (a^{2} - a b + b^{2}) + (a + b)$

$= (a + b) (a^{2} - a b + b^{2} + 1)$