What is expand (2x-1)^5 ?

The solution to expand (2x-1)^5 is 32x^5-80x^4+80x^3-40x^2+10x-1

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expand (2x-1)^5

expand

(2 x - 1)^{5}

32 x^{5} - 80 x^{4} + 80 x^{3} - 40 x^{2} + 10 x - 1

Solution steps

(2 x - 1)^{5}

Apply binomial theorem:

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

a = 2 x, b = - 1

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} (- 1)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} (- 1)^{0} : 32 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x)^{4} (- 1)^{1} : - 80 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} (- 1)^{2} : 80 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} (- 1)^{3} : - 40 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x)^{1} (- 1)^{4} : 10 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} (- 1)^{5} : - 1

= 32 x^{5} - 80 x^{4} + 80 x^{3} - 40 x^{2} + 10 x - 1

(4 x^{2} + 9 x - 7) - (- 7 x^{2} + 5 x - 1)

\frac{200}{3}

(x + 5) 2

(x^{2} - 5 x + 6) + (3 x^{2} - 8 x - 2)

(3 x - 1) (3 x + 1)

What is expand (2x-1)^5 ?
The solution to expand (2x-1)^5 is 32x^5-80x^4+80x^3-40x^2+10x-1