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Popular >

expand (x+1)^5

Solution

expand

(x + 1)^{5}

Solution

x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1

Solution steps

(x + 1)^{5}

Apply binomial theorem:

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

a = x, b = 1

= i = 0 \sum 5 (i 5) x^{(5 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} \cdot 1^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} \cdot 1^{1} : 5 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} \cdot 1^{2} : 10 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} \cdot 1^{3} : 10 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} \cdot 1^{4} : 5 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} \cdot 1^{5} : 1

= x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1

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Frequently Asked Questions (FAQ)

What is expand (x+1)^5 ?
The solution to expand (x+1)^5 is x^5+5x^4+10x^3+10x^2+5x+1