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Perfect Square Trinomials

Which of the ...

Question

Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ?

A

x^{2} + y^{2} + 2 x y

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B

x^{2} + y^{2} - x y

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C

x y^{2}

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D

3xy

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Solution

The correct option is D 3xy
$(x + y)^{3} - (x^{3} + y^{3})$
$(x^{3} + y^{3} + 3 x y (x + y) - x^{3} - y^{3}$
$3 x y (x + y)$
So, above term is factor of 3xy.
Answer (D) 3xy

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Q. Question 17
Which of the following is a factor of

(x + y)^{3} - (x^{3} + y^{3})

x^{2} + y^{2} + 2 x y

x^{2} + y^{2} - x y

x y^{2}

3 x y

Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ?

(a) $x^{2} + y^{2} + 2 x y$

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

(c) $x y^{2}$

(d) $3 x y$

Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ?

[\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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