展开 4(x^2+2x-4)^5

解答

展开

4 (x^{2} + 2 x - 4)^{5}

4 x^{10} + 40 x^{9} + 80 x^{8} - 320 x^{7} - 960 x^{6} + 1408 x^{5} + 3840 x^{4} - 5120 x^{3} - 5120 x^{2} + 10240 x - 4096

求解步骤

4 (x^{2} + 2 x - 4)^{5}

(x^{2} + 2 x - 4)^{5} = x^{10} + 10 x^{9} + 20 x^{8} - 80 x^{7} - 240 x^{6} + 352 x^{5} + 960 x^{4} - 1280 x^{3} - 1280 x^{2} + 2560 x - 1024

= 4 (x^{10} + 10 x^{9} + 20 x^{8} - 80 x^{7} - 240 x^{6} + 352 x^{5} + 960 x^{4} - 1280 x^{3} - 1280 x^{2} + 2560 x - 1024)

打开括号

= 4 x^{10} + 4 \cdot 10 x^{9} + 4 \cdot 20 x^{8} + 4 (- 80 x^{7}) + 4 (- 240 x^{6}) + 4 \cdot 352 x^{5} + 4 \cdot 960 x^{4} + 4 (- 1280 x^{3}) + 4 (- 1280 x^{2}) + 4 \cdot 2560 x + 4 (- 1024)

使用加减运算法则

+ (- a) = - a

= 4 x^{10} + 4 \cdot 10 x^{9} + 4 \cdot 20 x^{8} - 4 \cdot 80 x^{7} - 4 \cdot 240 x^{6} + 4 \cdot 352 x^{5} + 4 \cdot 960 x^{4} - 4 \cdot 1280 x^{3} - 4 \cdot 1280 x^{2} + 4 \cdot 2560 x - 4 \cdot 1024

化简

4 x^{10} + 4 \cdot 10 x^{9} + 4 \cdot 20 x^{8} - 4 \cdot 80 x^{7} - 4 \cdot 240 x^{6} + 4 \cdot 352 x^{5} + 4 \cdot 960 x^{4} - 4 \cdot 1280 x^{3} - 4 \cdot 1280 x^{2} + 4 \cdot 2560 x - 4 \cdot 1024 : 4 x^{10} + 40 x^{9} + 80 x^{8} - 320 x^{7} - 960 x^{6} + 1408 x^{5} + 3840 x^{4} - 5120 x^{3} - 5120 x^{2} + 10240 x - 4096

= 4 x^{10} + 40 x^{9} + 80 x^{8} - 320 x^{7} - 960 x^{6} + 1408 x^{5} + 3840 x^{4} - 5120 x^{3} - 5120 x^{2} + 10240 x - 4096

e x p an d (7 v^{2} - 4 v - 3) (6 v - 2^{^{'}})

e x p an d (5 x - 8 q^{2})^{2 (m - 2)}

e x p an d lo g_{6} (3 8 \cdot 7 \cdot 11)

e x p an d \frac{2}{( ( s + 2 ) \cdot ( s + 1 ) )}

e x p an d \frac{2}{4 + 2}