What is expand (1+x)^6 ?

The solution to expand (1+x)^6 is 1+6x+15x^2+20x^3+15x^4+6x^5+x^6

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expand (1+x)^6

expand

(1 + x)^{6}

1 + 6 x + 15 x^{2} + 20 x^{3} + 15 x^{4} + 6 x^{5} + x^{6}

Solution steps

(1 + x)^{6}

Apply binomial theorem:

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

a = 1, b = x

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} x^{i}

Expand summation

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

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} x^{0} : 1

Simplify

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

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} x^{2} : 15 x^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} x^{3} : 20 x^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} x^{4} : 15 x^{4}

Simplify

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

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} x^{6} : x^{6}

= 1 + 6 x + 15 x^{2} + 20 x^{3} + 15 x^{4} + 6 x^{5} + x^{6}

6 \cdot (- 4)

- \frac{12}{- 4}

(3 x - 8 y - 2 z) + (7 x + 3 y + z)

\frac{4}{5} \div \frac{1}{10}

\frac{5}{3}

What is expand (1+x)^6 ?
The solution to expand (1+x)^6 is 1+6x+15x^2+20x^3+15x^4+6x^5+x^6