What is expand (4d-3e)^5 ?

The solution to expand (4d-3e)^5 is 1024d^5-3840ed^4+5760e^2d^3-4320e^3d^2+1620e^4d-243e^5

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expand (4d-3e)^5

expand

(4 d - 3 e)^{5}

1024 d^{5} - 3840 e d^{4} + 5760 e^{2} d^{3} - 4320 e^{3} d^{2} + 1620 e^{4} d - 243 e^{5}

Solution steps

(4 d - 3 e)^{5}

Apply binomial theorem:

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

a = 4 d, b = - 3 e

= i = 0 \sum 5 (i 5) (4 d)^{(5 - i)} (- 3 e)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (4 d)^{5} (- 3 e)^{0} : 1024 d^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 d)^{4} (- 3 e)^{1} : - 3840 e d^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (4 d)^{3} (- 3 e)^{2} : 5760 e^{2} d^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (4 d)^{2} (- 3 e)^{3} : - 4320 e^{3} d^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (4 d)^{1} (- 3 e)^{4} : 1620 e^{4} d

\frac{5 !}{5 ! ( 5 - 5 ) !} (4 d)^{0} (- 3 e)^{5} = - 243 e^{5}

= 1024 d^{5} - 3840 e d^{4} + 5760 e^{2} d^{3} - 4320 e^{3} d^{2} + 1620 e^{4} d - 243 e^{5}

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

- \frac{42 x ^{5} ( x + 1 )}{55 y ^{2}}

\frac{15}{x ( x - 5 )}

(e^{x} - 5)^{3}

\frac{9 x ( 2 x + 5 )}{( 5 x - 2 ) ^{2}}

What is expand (4d-3e)^5 ?
The solution to expand (4d-3e)^5 is 1024d^5-3840ed^4+5760e^2d^3-4320e^3d^2+1620e^4d-243e^5