| (i) \[(2{{a}^{2}}+8a+3)\] |
| (ii) \[(6{{a}^{2}}+52a-5)\] |
| (iii) \[\text{(3a+5)}\] |
A) Only (i)
B) Both (i) and (ii)
C) Only (ii)
D) All (i), (ii) and (iii)
Correct Answer: B
Solution :
We have, \[12{{({{a}^{2}}+7a)}^{2}}-8({{a}^{2}}+7a)(2a-1)-15{{(2a-1)}^{2}}\] \[=12{{({{a}^{2}}+7a)}^{2}}-18({{a}^{2}}+7a)(2a-1)\] \[+10({{a}^{2}}+7a)(2a-1)-15{{(2a-1)}^{2}}\] \[=6({{a}^{2}}+7a)[2({{a}^{2}}+7a)-3(2a-1)]\] \[+5(2a-1)[2{{a}^{2}}+7a)-3(2a-1)]\] \[=(6{{a}^{2}}+42a)(2{{a}^{2}}+8a+3)\] \[+(10a-5)(2{{a}^{2}}+8a+3)\] \[=(6{{a}^{2}}+42a+10a-5)(2{{a}^{2}}+8a+3)\] \[=(6{{a}^{2}}+52a-5)(2{{a}^{2}}+8a+3)\]
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