What is expand (5w-2)^4 ?

The solution to expand (5w-2)^4 is 625w^4-1000w^3+600w^2-160w+16

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expand (5w-2)^4

expand

(5 w - 2)^{4}

625 w^{4} - 1000 w^{3} + 600 w^{2} - 160 w + 16

Solution steps

(5 w - 2)^{4}

Apply binomial theorem:

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

a = 5 w, b = - 2

= i = 0 \sum 4 (i 4) (5 w)^{(4 - i)} (- 2)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 w)^{4} (- 2)^{0} : 625 w^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 w)^{3} (- 2)^{1} : - 1000 w^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 w)^{2} (- 2)^{2} : 600 w^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 w)^{1} (- 2)^{3} : - 160 w

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 w)^{0} (- 2)^{4} : 16

= 625 w^{4} - 1000 w^{3} + 600 w^{2} - 160 w + 16

(x + 4)^{2} - 3

\frac{1}{4} \cdot \frac{5}{3}

4 a + 2 a

- 12 n - 20

(3 i) (- 1 + 6 i)

What is expand (5w-2)^4 ?
The solution to expand (5w-2)^4 is 625w^4-1000w^3+600w^2-160w+16