What is expand (4r-5a)^4 ?

The solution to expand (4r-5a)^4 is 256r^4-1280r^3a+2400r^2a^2-2000ra^3+625a^4

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expand (4r-5a)^4

expand

(4 r - 5 a)^{4}

256 r^{4} - 1280 r^{3} a + 2400 r^{2} a^{2} - 2000 r a^{3} + 625 a^{4}

Solution steps

(4 r - 5 a)^{4}

Apply binomial theorem:

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

a = 4 r, b = - 5 a

= i = 0 \sum 4 (i 4) (4 r)^{(4 - i)} (- 5 a)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (4 r)^{4} (- 5 a)^{0} : 256 r^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (4 r)^{3} (- 5 a)^{1} : - 1280 r^{3} a

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (4 r)^{2} (- 5 a)^{2} : 2400 r^{2} a^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (4 r)^{1} (- 5 a)^{3} : - 2000 r a^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (4 r)^{0} (- 5 a)^{4} : 625 a^{4}

= 256 r^{4} - 1280 r^{3} a + 2400 r^{2} a^{2} - 2000 r a^{3} + 625 a^{4}

(a + b)^{3} - a - b

(1 + \frac{x}{2} - \frac{2}{x})^{4}

\frac{4}{( x )}

12 c - 28 d + 52

(\frac{0.5 - 2 x}{0.5})^{2}

What is expand (4r-5a)^4 ?
The solution to expand (4r-5a)^4 is 256r^4-1280r^3a+2400r^2a^2-2000ra^3+625a^4