What is expand (2x-3)^5 ?

The solution to expand (2x-3)^5 is 32x^5-240x^4+720x^3-1080x^2+810x-243

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expand (2x-3)^5

expand

(2 x - 3)^{5}

32 x^{5} - 240 x^{4} + 720 x^{3} - 1080 x^{2} + 810 x - 243

Solution steps

(2 x - 3)^{5}

Apply binomial theorem:

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

a = 2 x, b = - 3

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} (- 3)^{0} : 32 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x)^{4} (- 3)^{1} : - 240 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} (- 3)^{2} : 720 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} (- 3)^{3} : - 1080 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x)^{1} (- 3)^{4} : 810 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} (- 3)^{5} : - 243

= 32 x^{5} - 240 x^{4} + 720 x^{3} - 1080 x^{2} + 810 x - 243

\frac{2 x ^{3}}{( x ^{- 1} ) ^{3}}

\frac{r + 3 s}{s + r} - \frac{3 s ^{2}}{s ^{2} - r ^{2}} + \frac{r}{s - r}

9 x + 36

(t + a)^{3}

16 - 104 x^{2} + 169 x^{4}

What is expand (2x-3)^5 ?
The solution to expand (2x-3)^5 is 32x^5-240x^4+720x^3-1080x^2+810x-243