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Question

Factorise: 4a2+9b2+16c2+12ab24bc16ac.

A
(2a+3b+4c)2
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B
(2a3b4c)2
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C
(2a+3b4c)2
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D
(2a3b+4c)2
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Solution

The correct option is C (2a+3b4c)2

Given:

4a2+9b2+16c2+12ab24bc16ac

Use the formula:

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

Simplify the equation.

4a2+9b2+16c2+12ab24bc16ac=(2a)2+(3b)2+(4c)2+2×2×3ab+2×(4)×3bc+2×(4)×2ac

=(2a+3b4c)2

Thus, the factor of the equation is (2a+3b4c)2.


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