| The factors of \[({{a}^{2}}+4{{b}^{2}}+4b-4ab-2a-8)\]are |
A) \[(a-2b-4)(a-2b+2)\]
B) \[(a-b+2)(a-4b-4)\]
C) \[(a+2b-4)(a+2b+2)\]
D) \[(a+2b-1)(a-2b+1)\]
Correct Answer: A
Solution :
| \[{{a}^{2}}+4{{b}^{2}}+4b-4ab-2a-8\] |
| On adding and subtracting 2a and 4b, we get |
| \[{{a}^{2}}+4{{b}^{2}}+4b-4ab-2a-8+2a-2a-4b+4b\] |
| \[=a\,(a-2b+2)-2b\,(a-2b+2)-4\,(a-2b+2)\] |
| \[=(a-2b+2)(a-2b-4)\] |
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