확장 x^2(3x^3-2)^4dx

해법

확장

x^{2} (3 x^{3} - 2)^{4} d x

81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

솔루션 단계

x^{2} (3 x^{3} - 2)^{4} d x

(3 x^{3} - 2)^{4} = 81 x^{12} - 216 x^{9} + 216 x^{6} - 96 x^{3} + 16

= x^{2} (81 x^{12} - 216 x^{9} + 216 x^{6} - 96 x^{3} + 16) d x

괄호 배포

= x^{2} d x \cdot 81 x^{12} + x^{2} d x (- 216 x^{9}) + x^{2} d x \cdot 216 x^{6} + x^{2} d x (- 96 x^{3}) + x^{2} d x \cdot 16

마이너스 플러스 규칙 적용

+ (- a) = - a

= 81 x^{12} x^{2} d x - 216 x^{9} x^{2} d x + 216 x^{6} x^{2} d x - 96 x^{3} x^{2} d x + 16 x^{2} d x

81 x^{12} x^{2} d x - 216 x^{9} x^{2} d x + 216 x^{6} x^{2} d x - 96 x^{3} x^{2} d x + 16 x^{2} d x

단순화하세요:

81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x

= 81 x^{14} d x - 216 x^{11} d x + 216 x^{8} d x - 96 x^{5} d x + 16 x^{2} d x