Question

Which of the following is a factor of (x+y) ^3- (x^3+y^3)?
(a) x² + y² + 2xy (b) x² + y² - xy (c) xy ^2(d) 3xy

Answer 1

Step-by-step explanation:

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(x+y)³-(x+y)(x²+y²-xy)

(x+y)(2xy+xy)

(x+y)(3xy)

=3xy

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@ Sweety Adihya

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Answer 2

Step-by-step explanation:

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$\bf \huge \: Question \:$

• Which of the following is a factor of (x+y) ^3- (x^3+y^3)?
• (a) x² + y² + 2xy (b) x² + y² - xy (c) xy ^2(d) 3xy

______________________

$\bf \huge \: To\: Find \:$

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

Now,

$\bf \:(x+ y)^3 – (x^3 + y^3) = (x + y) – (x + y)(x^2– xy + y^2)$

$\bf \:[using identity, a^3 + b^3 = (a + b)(a^2 -ab+ b^2)] = (x+ y)[(x+ y)^2 -(x^2 -xy+ y^2)]$

$\bf \:(x+ y)(x^2+ y^2+ 2xy- x^2+ xy- y°2)$

$\bf \:[using identity, (a + b)^2 = a^2 + b^2 + 2 ab)]$

$\bf \:= (x + y) (3xy)$

$\bf \:Hence,$

one of the factor of given polynomial is 3xy.