What is expand (2r-3s)^5 ?

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

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expand (2r-3s)^5

expand

(2 r - 3 s)^{5}

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

Solution steps

(2 r - 3 s)^{5}

Apply binomial theorem:

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

a = 2 r, b = - 3 s

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{x}{6} - \frac{x + 1}{6}

3 (x + 2)^{2} + 5

\frac{9}{4} \cdot 4

15 - 6

- 6 \cdot (- 12)

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