확장 x(x^2+x+1)^2

해법

확장

x (x^{2} + x + 1)^{2}

x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x

솔루션 단계

x (x^{2} + x + 1)^{2}

(x^{2} + x + 1)^{2} = x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1

= x (x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1)

괄호 배포

= x x^{4} + x \cdot 2 x^{3} + x \cdot 3 x^{2} + x \cdot 2 x + x \cdot 1

= x^{4} x + 2 x^{3} x + 3 x^{2} x + 2 xx + 1 \cdot x

x^{4} x + 2 x^{3} x + 3 x^{2} x + 2 xx + 1 \cdot x

단순화하세요:

x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x

= x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x