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Factorisation Using Algebraic Identities

The factors o...

Question

The factors of $x^{3} - 1 + y^{3} + 3 x y$ are

A

$(x - 1 + y) (x^{2} + 1 + y^{2} + x + y - x y)$

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B

$(x + y + 1) (x^{2} + y^{2} + 1 - x y - x - y)$

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C

$(x - 1 + y) (x^{2} - 1 - y^{2} + x + y + x y)$

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D

$3 (x + - 1) (x^{2} + y^{2} - 1)$

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Solution

The correct option is A
$(x - 1 + y) (x^{2} + 1 + y^{2} + x + y - x y)$

$x^{3} - 1 a + y^{3} + 3 x y = (x)^{3} + (- 1)^{3} + (y)^{3} - 3 \times x \times (- 1) \times y = (x - 1 + y) (x^{2} + 1 y^{2} + x + y - x y) = (x - 1 + y) (x^{2} + 1 + y^{2} + x + y - x y)$

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Similar questions

Q. Which of the following is a factor of (x + y)³ – (x³ + y³)?
(a) x² + 2xy + y²
(b) x² – xy + y²
(c) xy²
(d) 3xy

[\frac{x^{3} + y^{3}}{{(x - y)}^{2} + 3 x y}] \div [\frac{{(x + y)}^{2} - 3 x y}{x^{3} - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

[\frac{x^{3} + y^{3}}{(x - y)^{2} + 3 x y}] + [\frac{(x + y)^{2} - 3 x y}{x^{3} - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

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Q. Simplify the expression :

[\frac{x^{3} + y^{3}}{{(x - y)}^{2} + 3 x y}] \div [\frac{{(x + y)}^{2} - 3 x y}{x 3 - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

x + y = 1

x^{3} + y^{3} + 3 x y = . . . . . . . . . . . .

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