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

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

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expand (3x-5)^4

expand

(3 x - 5)^{4}

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

Solution steps

(3 x - 5)^{4}

Apply binomial theorem:

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

a = 3 x, b = - 5

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

2 π 7

6 x \cdot 42 x

2 x^{2} - 4 x - 96

(6 x - 6)^{2}

\frac{( 2 x ^{2} + 3 x + 1 )}{( x + 1 )}

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