展開する (5x^3+3x^2)(-4x+5)^{10}

解

展開する

(5 x^{3} + 3 x^{2}) (- 4 x + 5)^{10}

5242880 x^{13} - 62390272 x^{12} + 329318400 x^{11} - 1007616000 x^{10} + 1950720000 x^{9} - 2419200000 x^{8} + 1780800000 x^{7} - 480000000 x^{6} - 393750000 x^{5} + 453125000 x^{4} - 185546875 x^{3} + 29296875 x^{2}

解答ステップ

(5 x^{3} + 3 x^{2}) (- 4 x + 5)^{10}

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

分配法則を適用する:

a (b + c) = ab + a c

(- 4 x + 5)^{10} (5 x^{3} + 3 x^{2}) = (- 4 x + 5)^{10} \cdot 5 x^{3} + (- 4 x + 5)^{10} \cdot 3 x^{2}

= (- 4 x + 5)^{10} \cdot 5 x^{3} + (- 4 x + 5)^{10} \cdot 3 x^{2}

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

拡張

5 x^{3} (- 4 x + 5)^{10} : 5242880 x^{13} - 65536000 x^{12} + 368640000 x^{11} - 1228800000 x^{10} + 2688000000 x^{9} - 4032000000 x^{8} + 4200000000 x^{7} - 3000000000 x^{6} + 1406250000 x^{5} - 390625000 x^{4} + 48828125 x^{3}

= 5242880 x^{13} - 65536000 x^{12} + 368640000 x^{11} - 1228800000 x^{10} + 2688000000 x^{9} - 4032000000 x^{8} + 4200000000 x^{7} - 3000000000 x^{6} + 1406250000 x^{5} - 390625000 x^{4} + 48828125 x^{3} + 3 x^{2} (- 4 x + 5)^{10}

拡張

3 x^{2} (- 4 x + 5)^{10} : 3145728 x^{12} - 39321600 x^{11} + 221184000 x^{10} - 737280000 x^{9} + 1612800000 x^{8} - 2419200000 x^{7} + 2520000000 x^{6} - 1800000000 x^{5} + 843750000 x^{4} - 234375000 x^{3} + 29296875 x^{2}

= 5242880 x^{13} - 65536000 x^{12} + 368640000 x^{11} - 1228800000 x^{10} + 2688000000 x^{9} - 4032000000 x^{8} + 4200000000 x^{7} - 3000000000 x^{6} + 1406250000 x^{5} - 390625000 x^{4} + 48828125 x^{3} + 3145728 x^{12} - 39321600 x^{11} + 221184000 x^{10} - 737280000 x^{9} + 1612800000 x^{8} - 2419200000 x^{7} + 2520000000 x^{6} - 1800000000 x^{5} + 843750000 x^{4} - 234375000 x^{3} + 29296875 x^{2}

簡素化

5242880 x^{13} - 65536000 x^{12} + 368640000 x^{11} - 1228800000 x^{10} + 2688000000 x^{9} - 4032000000 x^{8} + 4200000000 x^{7} - 3000000000 x^{6} + 1406250000 x^{5} - 390625000 x^{4} + 48828125 x^{3} + 3145728 x^{12} - 39321600 x^{11} + 221184000 x^{10} - 737280000 x^{9} + 1612800000 x^{8} - 2419200000 x^{7} + 2520000000 x^{6} - 1800000000 x^{5} + 843750000 x^{4} - 234375000 x^{3} + 29296875 x^{2} : 5242880 x^{13} - 62390272 x^{12} + 329318400 x^{11} - 1007616000 x^{10} + 1950720000 x^{9} - 2419200000 x^{8} + 1780800000 x^{7} - 480000000 x^{6} - 393750000 x^{5} + 453125000 x^{4} - 185546875 x^{3} + 29296875 x^{2}

= 5242880 x^{13} - 62390272 x^{12} + 329318400 x^{11} - 1007616000 x^{10} + 1950720000 x^{9} - 2419200000 x^{8} + 1780800000 x^{7} - 480000000 x^{6} - 393750000 x^{5} + 453125000 x^{4} - 185546875 x^{3} + 29296875 x^{2}