What is expand (w-x)^5 ?

The solution to expand (w-x)^5 is w^5-5w^4x+10w^3x^2-10w^2x^3+5wx^4-x^5

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expand (w-x)^5

expand

(w - x)^{5}

w^{5} - 5 w^{4} x + 10 w^{3} x^{2} - 10 w^{2} x^{3} + 5 w x^{4} - x^{5}

Solution steps

(w - x)^{5}

Apply binomial theorem:

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

a = w, b = - x

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} w^{5} (- x)^{0} : w^{5}

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} w^{3} (- x)^{2} : 10 w^{3} x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} w^{2} (- x)^{3} : - 10 w^{2} x^{3}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} w^{0} (- x)^{5} : - x^{5}

= w^{5} - 5 w^{4} x + 10 w^{3} x^{2} - 10 w^{2} x^{3} + 5 w x^{4} - x^{5}

\frac{0}{83}

\frac{2 + 3}{8 + 4 3}

(- 3 - i)^{3}

11664

1 0^{2.4}

What is expand (w-x)^5 ?
The solution to expand (w-x)^5 is w^5-5w^4x+10w^3x^2-10w^2x^3+5wx^4-x^5