What is the value of $a^2 +4b^2 +9c^2 -

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

What is the value of $a^2 +4b^2 +9c^2 - 4ab +12bc - 6ca $ ?

Options:

$(a + 2b - 3c)^2$

$(2a - b -3c)^2$

$(2b - a - 3c)^2$

$(a - 2b - 3c)^2$

Correct Answer:

$(a - 2b - 3c)^2$

Explanation:

We know that,

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

a²+ 4b² + 9c² - 4ab + 12bc - 6ca

= a²+ 4b² + 9c² - 4ab + 12bc - 6ca

= (a)² + (-2b)² +(-3c)² +2[ a(-2b) + (-2b)(-3c) + a(-3c) ]

a²+ 4b² + 9c² - 4ab + 12bc - 6ca = (a - 2b - 3c)²