MCQ
The value of $(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3$ is:
- ✓$3(a + b) (b + c) (c + a) (a - b) (b - c) (c - a)$
- B$3(a - b) (b - c) (c - a)$
- C$3(a + b) (b + c) (c + a)$
- DNone of these.
✓
Answer
Correct option: A.
$3(a + b) (b + c) (c + a) (a - b) (b - c) (c - a)$
$(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3$
Here,$a^2-b^2+b^2-c^2+c^2-a^2=0$
Therefore,
$(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=3(a^2-b^2)(b^2-c^2)(c^2-a^2)$
${[\text { Since } x^3+y^3+z^3=3 x y z \text { if } x+y+z=0]}$
$(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=$
$3(a+b)(b+c)(c+a)(a-b)(b-c)(c-a)$
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