What is expand (3-5x)^4 ?

The solution to expand (3-5x)^4 is 81-540x+1350x^2-1500x^3+625x^4

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expand (3-5x)^4

expand

(3 - 5 x)^{4}

81 - 540 x + 1350 x^{2} - 1500 x^{3} + 625 x^{4}

Solution steps

(3 - 5 x)^{4}

Apply binomial theorem:

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

a = 3, b = - 5 x

= i = 0 \sum 4 (i 4) \cdot 3^{(4 - i)} (- 5 x)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 3^{4} (- 5 x)^{0} : 81

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 3^{3} (- 5 x)^{1} : - 540 x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 3^{2} (- 5 x)^{2} : 1350 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 3^{1} (- 5 x)^{3} : - 1500 x^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 3^{0} (- 5 x)^{4} : 625 x^{4}

= 81 - 540 x + 1350 x^{2} - 1500 x^{3} + 625 x^{4}

(1 - i 3)^{- 2}

(2 x - 12)^{2}

\frac{- x}{x ^{2}}

6 (x + 2)

\frac{12 a ^{4}}{3 ( a ^{5} ) ^{3}}

What is expand (3-5x)^4 ?
The solution to expand (3-5x)^4 is 81-540x+1350x^2-1500x^3+625x^4