What is expand (a-b)^6 ?

The solution to expand (a-b)^6 is a^6-6a^5b+15a^4b^2-20a^3b^3+15a^2b^4-6ab^5+b^6

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expand (a-b)^6

expand

(a - b)^{6}

a^{6} - 6 a^{5} b + 15 a^{4} b^{2} - 20 a^{3} b^{3} + 15 a^{2} b^{4} - 6 a b^{5} + b^{6}

Solution steps

(a - b)^{6}

Apply binomial theorem:

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

a = a, b = - b

= i = 0 \sum 6 (i 6) a^{(6 - i)} (- b)^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} a^{6} (- b)^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} a^{5} (- b)^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} a^{4} (- b)^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} a^{3} (- b)^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} a^{2} (- b)^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} a^{1} (- b)^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} a^{0} (- b)^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} a^{6} (- b)^{0} : a^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} a^{5} (- b)^{1} : - 6 a^{5} b

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} a^{4} (- b)^{2} : 15 a^{4} b^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} a^{3} (- b)^{3} : - 20 a^{3} b^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} a^{2} (- b)^{4} : 15 a^{2} b^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} a^{1} (- b)^{5} : - 6 a b^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} a^{0} (- b)^{6} : b^{6}

= a^{6} - 6 a^{5} b + 15 a^{4} b^{2} - 20 a^{3} b^{3} + 15 a^{2} b^{4} - 6 a b^{5} + b^{6}

- 4 ∣ 5 + (- 3) ∣

(- \frac{2}{5})^{2}

- 4 (2 x + 3)

(- x - 1)^{3}

(10 + i)^{2}

What is expand (a-b)^6 ?
The solution to expand (a-b)^6 is a^6-6a^5b+15a^4b^2-20a^3b^3+15a^2b^4-6ab^5+b^6