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Tentukan suku keempat dari (x−3y)6.

Pertanyaan

Tentukan suku keempat dari open parentheses x minus 3 y close parentheses to the power of 6.

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

diperoleh suku keempat dari open parentheses x minus 3 y close parentheses to the power of 6 adalah 1215 x squared y to the power of 4.

Pembahasan

Gunakan konsep binomial Newton.

Suku ke-r dari pemangkatan open parentheses A plus B close parentheses to the power of n equals straight C subscript open parentheses n comma space r close parentheses end subscript times A to the power of n italic minus r end exponent times B to the power of r

Akan ditentukan suku keempat dari open parentheses x minus 3 y close parentheses to the power of 6.

table attributes columnalign right center left columnspacing 2px end attributes row cell straight C subscript open parentheses 6 comma space 4 close parentheses end subscript times open parentheses x close parentheses to the power of 6 minus 4 end exponent times open parentheses negative 3 y close parentheses to the power of 4 end cell equals cell fraction numerator 6 factorial over denominator open parentheses 6 minus 4 close parentheses factorial times 4 factorial end fraction times x squared times 81 y to the power of 4 end cell row blank equals cell fraction numerator up diagonal strike 6 cubed cross times 5 cross times up diagonal strike 4 factorial end strike over denominator up diagonal strike 2 cross times up diagonal strike 4 factorial end strike end fraction times x squared times 81 y to the power of 4 end cell row blank equals cell 15 times x squared times 81 y to the power of 4 end cell row cell straight C subscript open parentheses 6 comma space 4 close parentheses end subscript times open parentheses x close parentheses to the power of 6 minus 4 end exponent times open parentheses negative 3 y close parentheses to the power of 4 end cell equals cell 1215 x squared y to the power of 4 end cell end table 

Jadi, diperoleh suku keempat dari open parentheses x minus 3 y close parentheses to the power of 6 adalah 1215 x squared y to the power of 4.

229

5.0 (2 rating)

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