Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

What is the value of $(a^2 +b^2 +4c^2 -ab -2ca)( a + b + 2c) ?$

Options:

$a^3 + b^3 +8c^3 - 8abc $

$a^3 + b^3 +8c^3 - 4abc $

$4a^3 + b^3 +8c^3 - 9abc $

$a^3 + b^3 +8c^3 - 6abc $

Correct Answer:

$a^3 + b^3 +8c^3 - 6abc $

Explanation:

We know,

 x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)

 (a + b + 2c) (a2 + b2 + 4c2 – ab – 2bc – 2ca)

= a3 + b3 + 8c3 – 6abc