What is expand (x-y)^7 ?

The solution to expand (x-y)^7 is x^7-7x^6y+21x^5y^2-35x^4y^3+35x^3y^4-21x^2y^5+7xy^6-y^7

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expand (x-y)^7

expand

(x - y)^{7}

x^{7} - 7 x^{6} y + 21 x^{5} y^{2} - 35 x^{4} y^{3} + 35 x^{3} y^{4} - 21 x^{2} y^{5} + 7 x y^{6} - y^{7}

Solution steps

(x - y)^{7}

Apply binomial theorem:

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

a = x, b = - y

= i = 0 \sum 7 (i 7) x^{(7 - i)} (- y)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} x^{7} (- y)^{0} : x^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} x^{6} (- y)^{1} : - 7 x^{6} y

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} x^{5} (- y)^{2} : 21 x^{5} y^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} x^{4} (- y)^{3} : - 35 x^{4} y^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} x^{3} (- y)^{4} : 35 x^{3} y^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} x^{2} (- y)^{5} : - 21 x^{2} y^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} x^{1} (- y)^{6} : 7 x y^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} x^{0} (- y)^{7} : - y^{7}

= x^{7} - 7 x^{6} y + 21 x^{5} y^{2} - 35 x^{4} y^{3} + 35 x^{3} y^{4} - 21 x^{2} y^{5} + 7 x y^{6} - y^{7}

3 \cdot 11

(6 + 5 i) \cdot (2 - 3 i)

(3 x + 5)^{2} + (2 x - 3)^{2} - 13 x^{2} - 34

\frac{1 + 2 i}{1 - 2 i} + \frac{2 + i}{1 + 2 i}

32 n^{\frac{3}{2}}

What is expand (x-y)^7 ?
The solution to expand (x-y)^7 is x^7-7x^6y+21x^5y^2-35x^4y^3+35x^3y^4-21x^2y^5+7xy^6-y^7