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}

(y + h)^{3}

\frac{2 π}{\frac{4 π}{7}}

x^{6} - 6 x^{5} - x^{4} + 6 x^{3}

\frac{a + x}{a - x} - \frac{a - x}{a + x}

v^{19}

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