What is expand (3-2x)^6 ?

The solution to expand (3-2x)^6 is 729-2916x+4860x^2-4320x^3+2160x^4-576x^5+64x^6

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expand (3-2x)^6

expand

(3 - 2 x)^{6}

729 - 2916 x + 4860 x^{2} - 4320 x^{3} + 2160 x^{4} - 576 x^{5} + 64 x^{6}

Solution steps

(3 - 2 x)^{6}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 3, b = - 2 x

= i = 0 \sum 6 (i 6) \cdot 3^{(6 - i)} (- 2 x)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 3^{6} (- 2 x)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 3^{5} (- 2 x)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 3^{4} (- 2 x)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 3^{3} (- 2 x)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 3^{2} (- 2 x)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 3^{1} (- 2 x)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 3^{0} (- 2 x)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 3^{6} (- 2 x)^{0} : 729

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 3^{5} (- 2 x)^{1} : - 2916 x

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 3^{4} (- 2 x)^{2} : 4860 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 3^{3} (- 2 x)^{3} : - 4320 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 3^{2} (- 2 x)^{4} : 2160 x^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 3^{1} (- 2 x)^{5} : - 576 x^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 3^{0} (- 2 x)^{6} : 64 x^{6}

= 729 - 2916 x + 4860 x^{2} - 4320 x^{3} + 2160 x^{4} - 576 x^{5} + 64 x^{6}

(7 x - 3)^{6}

\frac{( \frac{1}{x ^{2}} - \frac{1}{x} )}{( \frac{1}{x ^{2}} + \frac{1}{x} )}

\frac{x + 3}{x ^{2} + 5 x + 6}

1.5 \cdot 1 0^{5}

\frac{1}{cos ( x )} + \frac{sin ( x )}{cos ( x )}

What is expand (3-2x)^6 ?
The solution to expand (3-2x)^6 is 729-2916x+4860x^2-4320x^3+2160x^4-576x^5+64x^6