What is expand (1+sqrt(x))^7 ?

The solution to expand (1+sqrt(x))^7 is 1+7sqrt(x)+21x+35xsqrt(x)+35x^2+21x^2sqrt(x)+7x^3+x^3sqrt(x)

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expand (1+sqrt(x))^7

expand

(1 + x)^{7}

1 + 7 x + 21 x + 35 x x + 35 x^{2} + 21 x^{2} x + 7 x^{3} + x^{3} x

Solution steps

(1 + x)^{7}

Apply binomial theorem:

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

a = 1, b = x

= i = 0 \sum 7 (i 7) \cdot 1^{(7 - i)} (x)^{i}

Expand summation

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

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} \cdot 1^{7} (x)^{0} : 1

Simplify

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

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} \cdot 1^{5} (x)^{2} : 21 x

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} \cdot 1^{4} (x)^{3} : 35 (x)^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} \cdot 1^{3} (x)^{4} : 35 x^{2}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} \cdot 1^{2} (x)^{5} : 21 (x)^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} \cdot 1^{1} (x)^{6} : 7 x^{3}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} \cdot 1^{0} (x)^{7} : (x)^{7}

= 1 + 7 x + 21 x + 35 (x)^{3} + 35 x^{2} + 21 (x)^{5} + 7 x^{3} + (x)^{7}

(x)^{3} = x x

(x)^{5} = x^{2} x

(x)^{7} = x^{3} x

= 1 + 7 x + 21 x + 35 x x + 35 x^{2} + 21 x^{2} x + 7 x^{3} + x^{3} x

(1 + x)^{6}

\frac{2 ( s ^{2} + 4 )}{s ^{2} + 2}

(x + 2) (x - 2) (x + \frac{17}{10}) (x - \frac{17}{10})

x 2 - 1.695 x + 0.2583

(9 + 3) (7 + 2)

What is expand (1+sqrt(x))^7 ?
The solution to expand (1+sqrt(x))^7 is 1+7sqrt(x)+21x+35xsqrt(x)+35x^2+21x^2sqrt(x)+7x^3+x^3sqrt(x)