What is expand (5x-9)^4 ?

The solution to expand (5x-9)^4 is 625x^4-4500x^3+12150x^2-14580x+6561

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expand (5x-9)^4

expand

(5 x - 9)^{4}

625 x^{4} - 4500 x^{3} + 12150 x^{2} - 14580 x + 6561

Solution steps

(5 x - 9)^{4}

Apply binomial theorem:

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

a = 5 x, b = - 9

= i = 0 \sum 4 (i 4) (5 x)^{(4 - i)} (- 9)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (5 x)^{4} (- 9)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (5 x)^{3} (- 9)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (5 x)^{2} (- 9)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (5 x)^{1} (- 9)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (5 x)^{0} (- 9)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 x)^{4} (- 9)^{0} : 625 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x)^{3} (- 9)^{1} : - 4500 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x)^{2} (- 9)^{2} : 12150 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x)^{1} (- 9)^{3} : - 14580 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 x)^{0} (- 9)^{4} : 6561

= 625 x^{4} - 4500 x^{3} + 12150 x^{2} - 14580 x + 6561

6 x - 4 y - x^{2} - 2 y^{2}

40 + 32 + (6 x^{8})

3 j^{112} + 3 j^{39}

2 cos^{2} (a) - 1

x^{4} - 50 x^{2} + 625

What is expand (5x-9)^4 ?
The solution to expand (5x-9)^4 is 625x^4-4500x^3+12150x^2-14580x+6561