Thực hành 2:Sử dụng tam giác Pascal, hãy khai triển:a) $(2x+1)^{6}$b) $(2x+1)^{6}$

a) Sử dụng tam giác Pascal, ta có:
$(2x+1)^{6} = \binom{6}{0}(2x)^{6}(1)^{0} + \binom{6}{1}(2x)^{5}(1)^{1} + \binom{6}{2}(2x)^{4}(1)^{2} + \binom{6}{3}(2x)^{3}(1)^{3} + \binom{6}{4}(2x)^{2}(1)^{4} + \binom{6}{5}(2x)^{1}(1)^{5} + \binom{6}{6}(2x)^{0}(1)^{6}$
$= 1(64x^{6}) + 6(32x^{5}) + 15(16x^{4}) + 20(8x^{3}) + 15(4x^{2}) + 6(2x) + 1$

b) Sử dụng tam giác Pascal, ta có:
$(2x+1)^{6} = \binom{6}{0}(2x)^{6}(1)^{0} + \binom{6}{1}(2x)^{5}(1)^{1} + \binom{6}{2}(2x)^{4}(1)^{2} + \binom{6}{3}(2x)^{3}(1)^{3} + \binom{6}{4}(2x)^{2}(1)^{4} +$
$\binom{6}{5}(2x)^{1}(1)^{5} + \binom{6}{6}(2x)^{0}(1)^{6}$
$= 1(64x^{6}) + 6(32x^{5}) + 15(16x^{4}) + 20(8x^{3}) + 15(4x^{2}) + 6(2x) + 1$


Đáp án:
a) $(2x+1)^{6} = 64x^{6} + 192x^{5} + 240x^{4} + 160x^{3} + 60x^{2} + 12x + 1$
b) $(2x+1)^{6} = 64x^{6} + 192x^{5} + 240x^{4} + 160x^{3} + 60x^{2} + 12x + 1$