What is expand (a-b)^7 ?

The solution to expand (a-b)^7 is a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7

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expand (a-b)^7

expand

(a - b)^{7}

a^{7} - 7 a^{6} b + 21 a^{5} b^{2} - 35 a^{4} b^{3} + 35 a^{3} b^{4} - 21 a^{2} b^{5} + 7 a b^{6} - b^{7}

Solution steps

(a - b)^{7}

Apply binomial theorem:

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

a = a, b = - b

= i = 0 \sum 7 (i 7) a^{(7 - i)} (- b)^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} a^{7} (- b)^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} a^{6} (- b)^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} a^{5} (- b)^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} a^{4} (- b)^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} a^{3} (- b)^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} a^{2} (- b)^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} a^{1} (- b)^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} a^{0} (- b)^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} a^{7} (- b)^{0} : a^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} a^{6} (- b)^{1} : - 7 a^{6} b

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} a^{5} (- b)^{2} : 21 a^{5} b^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} a^{4} (- b)^{3} : - 35 a^{4} b^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} a^{3} (- b)^{4} : 35 a^{3} b^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} a^{2} (- b)^{5} : - 21 a^{2} b^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} a^{1} (- b)^{6} : 7 a b^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} a^{0} (- b)^{7} : - b^{7}

= a^{7} - 7 a^{6} b + 21 a^{5} b^{2} - 35 a^{4} b^{3} + 35 a^{3} b^{4} - 21 a^{2} b^{5} + 7 a b^{6} - b^{7}

\frac{( x ^{- 2} - 6 x ^{- 3} )}{( 6 x ^{- 2} - 36 x ^{- 3} )}

\frac{- 2 - [ 7 - ( - 1 ) ^{4} ( x ^{6} ) ^{1} ]}{( - 3 )}

6 (x + h)^{3}

(a^{2} - a + b) (a + b - 2)

(\frac{( x + h ) ^{3}}{2}) - (\frac{x ^{3}}{2})

What is expand (a-b)^7 ?
The solution to expand (a-b)^7 is a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7