What is expand (x+h)^6 ?

The solution to expand (x+h)^6 is x^6+6x^5h+15x^4h^2+20x^3h^3+15x^2h^4+6xh^5+h^6

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expand (x+h)^6

expand

(x + h)^{6}

x^{6} + 6 x^{5} h + 15 x^{4} h^{2} + 20 x^{3} h^{3} + 15 x^{2} h^{4} + 6 x h^{5} + h^{6}

Solution steps

(x + h)^{6}

Apply binomial theorem:

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

a = x, b = h

= i = 0 \sum 6 (i 6) x^{(6 - i)} h^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} x^{6} h^{0} : x^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} x^{5} h^{1} : 6 x^{5} h

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} x^{4} h^{2} : 15 x^{4} h^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} x^{3} h^{3} : 20 x^{3} h^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} x^{2} h^{4} : 15 x^{2} h^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} x^{1} h^{5} : 6 x h^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} x^{0} h^{6} : h^{6}

= x^{6} + 6 x^{5} h + 15 x^{4} h^{2} + 20 x^{3} h^{3} + 15 x^{2} h^{4} + 6 x h^{5} + h^{6}

8 x^{3} - 3 50 x

(2 x^{2} - 4 x) (6 x - 7)

(- 7 a^{4} b c^{3}) (5 a b^{4} c^{2})

(mn - x y)^{2}

(- 3) - 6

What is expand (x+h)^6 ?
The solution to expand (x+h)^6 is x^6+6x^5h+15x^4h^2+20x^3h^3+15x^2h^4+6xh^5+h^6