展开 a(x^2+2x+2)^2

解答

展开

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

a x^{4} + 4 a x^{3} + 8 a x^{2} + 8 a x + 4 a

求解步骤

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

(x^{2} + 2 x + 2)^{2} = x^{4} + 4 x^{3} + 8 x^{2} + 8 x + 4

= a (x^{4} + 4 x^{3} + 8 x^{2} + 8 x + 4)

打开括号

= a x^{4} + a \cdot 4 x^{3} + a \cdot 8 x^{2} + a \cdot 8 x + a \cdot 4

= a x^{4} + 4 a x^{3} + 8 a x^{2} + 8 a x + 4 a

e x p an d 10 (3 - 11)

e x p an d \frac{3 x ^{2} - 3 x + 2}{( x - 1 ) ^{3} ( x + 1 )}

e x p an d \frac{( 1 + x ^{2} ) ^{(\frac{3}{2})} - 1}{3}

e x p an d - 2 (5 x - 4 y = - 9)

e x p an d ((- 1)^{k + 1} \cdot (k + 1)) \cdot 4