What is expand (-p+q)^5 ?

The solution to expand (-p+q)^5 is -p^5+5p^4q-10p^3q^2+10p^2q^3-5pq^4+q^5

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expand (-p+q)^5

expand

(- p + q)^{5}

- p^{5} + 5 p^{4} q - 10 p^{3} q^{2} + 10 p^{2} q^{3} - 5 p q^{4} + q^{5}

Solution steps

(- p + q)^{5}

Apply binomial theorem:

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

a = - p, b = q

= i = 0 \sum 5 (i 5) (- p)^{(5 - i)} q^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (- p)^{5} q^{0} : - p^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (- p)^{4} q^{1} : 5 p^{4} q

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (- p)^{3} q^{2} : - 10 p^{3} q^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (- p)^{2} q^{3} : 10 p^{2} q^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (- p)^{1} q^{4} : - 5 p q^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (- p)^{0} q^{5} : q^{5}

= - p^{5} + 5 p^{4} q - 10 p^{3} q^{2} + 10 p^{2} q^{3} - 5 p q^{4} + q^{5}

(6 - x)^{2}

4 - x - \frac{x}{2 4 - x}

- (- x)

(- 7 + 5 i)^{2}

18 + 52

What is expand (-p+q)^5 ?
The solution to expand (-p+q)^5 is -p^5+5p^4q-10p^3q^2+10p^2q^3-5pq^4+q^5