확장 x^3(5x^2-x+1)^2

해법

확장

x^{3} (5 x^{2} - x + 1)^{2}

25 x^{7} - 10 x^{6} + 11 x^{5} - 2 x^{4} + x^{3}

솔루션 단계

x^{3} (5 x^{2} - x + 1)^{2}

(5 x^{2} - x + 1)^{2} = 25 x^{4} - 10 x^{3} + 11 x^{2} - 2 x + 1

= x^{3} (25 x^{4} - 10 x^{3} + 11 x^{2} - 2 x + 1)

괄호 배포

= x^{3} \cdot 25 x^{4} + x^{3} (- 10 x^{3}) + x^{3} \cdot 11 x^{2} + x^{3} (- 2 x) + x^{3} \cdot 1

마이너스 플러스 규칙 적용

+ (- a) = - a

= 25 x^{4} x^{3} - 10 x^{3} x^{3} + 11 x^{3} x^{2} - 2 x^{3} x + 1 \cdot x^{3}

25 x^{4} x^{3} - 10 x^{3} x^{3} + 11 x^{3} x^{2} - 2 x^{3} x + 1 \cdot x^{3}

단순화하세요:

25 x^{7} - 10 x^{6} + 11 x^{5} - 2 x^{4} + x^{3}

= 25 x^{7} - 10 x^{6} + 11 x^{5} - 2 x^{4} + x^{3}