What is expand (7x-3)^6 ?

The solution to expand (7x-3)^6 is 117649x^6-302526x^5+324135x^4-185220x^3+59535x^2-10206x+729

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expand (7x-3)^6

expand

(7 x - 3)^{6}

117649 x^{6} - 302526 x^{5} + 324135 x^{4} - 185220 x^{3} + 59535 x^{2} - 10206 x + 729

Solution steps

(7 x - 3)^{6}

Apply binomial theorem:

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

a = 7 x, b = - 3

= i = 0 \sum 6 (i 6) (7 x)^{(6 - i)} (- 3)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} (7 x)^{6} (- 3)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} (7 x)^{5} (- 3)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} (7 x)^{4} (- 3)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} (7 x)^{3} (- 3)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} (7 x)^{2} (- 3)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} (7 x)^{1} (- 3)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} (7 x)^{0} (- 3)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} (7 x)^{6} (- 3)^{0} : 117649 x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} (7 x)^{5} (- 3)^{1} : - 302526 x^{5}

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} (7 x)^{4} (- 3)^{2} : 324135 x^{4}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} (7 x)^{3} (- 3)^{3} : - 185220 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} (7 x)^{2} (- 3)^{4} : 59535 x^{2}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} (7 x)^{1} (- 3)^{5} : - 10206 x

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} (7 x)^{0} (- 3)^{6} : 729

= 117649 x^{6} - 302526 x^{5} + 324135 x^{4} - 185220 x^{3} + 59535 x^{2} - 10206 x + 729

\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 )}

2 x^{4} + 5 x^{3}

What is expand (7x-3)^6 ?
The solution to expand (7x-3)^6 is 117649x^6-302526x^5+324135x^4-185220x^3+59535x^2-10206x+729