What is expand (a-b)^5 ?

The solution to expand (a-b)^5 is a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5

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expand (a-b)^5

expand

(a - b)^{5}

a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}

Solution steps

(a - b)^{5}

Apply binomial theorem:

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

a = a, b = - b

= i = 0 \sum 5 (i 5) a^{(5 - i)} (- b)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} a^{5} (- b)^{0} : a^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} a^{4} (- b)^{1} : - 5 a^{4} b

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} a^{3} (- b)^{2} : 10 a^{3} b^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} a^{2} (- b)^{3} : - 10 a^{2} b^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} a^{1} (- b)^{4} : 5 a b^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} a^{0} (- b)^{5} : - b^{5}

= a^{5} - 5 a^{4} b + 10 a^{3} b^{2} - 10 a^{2} b^{3} + 5 a b^{4} - b^{5}

2 x (x - 1)

(x^{2} - 4) (x^{2} + 6 x + 9)

\frac{x ^{2} - 8}{x ^{2} - 10 x + 21} + \frac{5 - 2 x}{x ^{2} - 10 x + 21}

\frac{30}{7}

(3 x + 5)^{3}

What is expand (a-b)^5 ?
The solution to expand (a-b)^5 is a^5-5a^4b+10a^3b^2-10a^2b^3+5ab^4-b^5