What is expand (x+h)^7 ?

The solution to expand (x+h)^7 is x^7+7x^6h+21x^5h^2+35x^4h^3+35x^3h^4+21x^2h^5+7xh^6+h^7

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expand (x+h)^7

expand

(x + h)^{7}

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

Solution steps

(x + h)^{7}

Apply binomial theorem:

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

a = x, b = h

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

0^{9}

- 2 x^{2} - 4 x - 2 x^{2} - 2 x - 5

\frac{4 x ^{2}}{12 x ^{2} - 4}

\frac{26}{8}

9 - (- 7)

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