Mathematics
Grade10
Easy
Question
Determine the independent term of x7 in the expansion of (3x2 + 4)12.
- 220 × 46
- 230
- 548× 3!
- 220 × 36 × 46
The correct answer is: 220 × 36 × 46
By using Binomial theorem
![sum for k equals 0 of open parentheses n to the power of k close parentheses x to the power of k y to the power of n times k end exponent equals n to the power of 0 x to the power of 0 y to the power of n plus n to the power of 1 x to the power of 1 y to the power of n times 1 end exponent plus n squared x squared y to the power of n times 2 end exponent plus horizontal ellipsis plus n to the power of n x to the power of n y to the power of 0 comma text where end text open parentheses n to the power of k close parentheses](data:image/png;base64,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)
![equals fraction numerator n factorial over denominator k factorial left parenthesis n minus k right parenthesis factorial end fraction times text Now, end text T subscript r plus 1 end subscript equals C presuperscript n subscript r a to the power of n asterisk times r end exponent b to the power of r comma T subscript 9 plus 1 end subscript equals C presuperscript 12 subscript 6 a to the power of 12 minus 6 end exponent b to the power of 6 equals 220 asterisk times open parentheses 3 x squared close parentheses to the power of 6 asterisk times left parenthesis 4 right parenthesis to the power of 6 equals 220 asterisk times 3 to the power of 6 asterisk times 4 to the power of 6 times](data:image/png;base64,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)
Hence the coefficient is ![220 asterisk times 3 to the power of 6 asterisk times 4 to the power of 6](data:image/png;base64,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)
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![left parenthesis x minus y right parenthesis to the power of 14](data:image/png;base64,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)
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