The value of (a^2-b^2 )^3+ (b^2-c^2 )^3+ (c^2-a^2 )^3 (a-b)^3+(b-… - Vidyadip

MCQ

The value of $\frac{\left(a^2-b^2\right)^3+\left(b^2-c^2\right)^3+\left(c^2-a^2\right)^3}{(a-b)^3+(b-c)^3+(c-a)^3}$ is

A
$3(a - b)(b - c)(c - a)$
✓
$(a + b)(b + c)(c + a)$
C
$3(a + b)(b + c)(c + a)(a - b)(b - c)(c - a)$
D
$2(a - b)(b - c)(c - a)$

✓

Answer

Correct option: B.

$(a + b)(b + c)(c + a)$

$\frac{\left(a^2-b^2\right)^3+\left(b^2-c^2\right)^3+\left(c^2-a^2\right)^3}{(a-b)^3+\left(b-c)^3+(c-a)^3\right.}$
$=\frac{3\left(a^2-b^2\right)\left(b^2-c^2\right)\left(c^2-a^2\right)}{3(a-b)(b-c)(c-a)}[$ Since $x^3+y^3+z^3=3 x y z,$ if $x+y+z=0]$
$=\frac{3(a-b)(a+b)(b-c)(b+c)(c-a)(c+a)}{3(a-b)(b-c)(c-a)}$
$=(a+b)(b+c)(c+a)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Model Paper 1→Model Paper 1 — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

In the given figure, $AD$ is a diameter of the circle with centre $O.$ Chords $AB, BC$ and $CD$ are equal. If $\angle\text{DEF}=110^\circ,$ then $\angle\text{FAB}$ is equal to:

One chord of a circle is known to be $10\ cm.$ The radius of this circle must be:

Any point of the form $(a, -a)$ always lie on the graph of the equation.

The side BC of $\triangle A B C$ is produced to a point D. The bisector of $\angle A$ meets side BC in L. If $\angle A B C=30^{\circ}$ and $\angle A C D=115^{\circ}$, then $\angle A L C=$

Line segments AB and CD intersect at O such that AC|| DB . If $\angle C A B=45^{\circ}$ and $\angle C D B=55^{\circ}$, then $\angle B O D=$

Write the correct answer in the following: The sides of a triangle are $35\ cm, 54\ cm$ and $61\ cm$, respectively. The length of its longest altitude:

In the given figure, equilateral $\triangle\text{ABC}$ is inscribed in a circle and $ABCD$ is a quadrilateral, as shown. Then, $\angle\text{BDC}=?$

In the figure, if $\angle\text{DAB}=60^\circ,\angle\text{ABD}=50^\circ$ then $\angle\text{ACB}$ is equal to:

Which of the following is not a solution of $3x + 4y = 12?$

In figure, if $\text{AE}||\text{DC}$ and $AB = AC$, the value of $\angle\text{ABD}$ is: