What is expand (3x-1)^5 ?

The solution to expand (3x-1)^5 is 243x^5-405x^4+270x^3-90x^2+15x-1

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expand (3x-1)^5

expand

(3 x - 1)^{5}

243 x^{5} - 405 x^{4} + 270 x^{3} - 90 x^{2} + 15 x - 1

Solution steps

(3 x - 1)^{5}

Apply binomial theorem:

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

a = 3 x, b = - 1

= i = 0 \sum 5 (i 5) (3 x)^{(5 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x)^{5} (- 1)^{0} : 243 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x)^{4} (- 1)^{1} : - 405 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x)^{3} (- 1)^{2} : 270 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x)^{2} (- 1)^{3} : - 90 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x)^{1} (- 1)^{4} : 15 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (3 x)^{0} (- 1)^{5} : - 1

= 243 x^{5} - 405 x^{4} + 270 x^{3} - 90 x^{2} + 15 x - 1

\frac{x ^{2} + 3 x - 54}{x ^{2} + 4 x - 45}

\frac{1}{8} \div \frac{3}{4}

11 \frac{1}{4}

3 \cdot \frac{3}{5}

lo g_{64} (\frac{1}{8})

What is expand (3x-1)^5 ?
The solution to expand (3x-1)^5 is 243x^5-405x^4+270x^3-90x^2+15x-1