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Popular >

expand (a+1)^4

Solution

expand

(a + 1)^{4}

Solution

a^{4} + 4 a^{3} + 6 a^{2} + 4 a + 1

Solution steps

(a + 1)^{4}

Apply binomial theorem:

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

a = a, b = 1

= i = 0 \sum 4 (i 4) a^{(4 - i)} \cdot 1^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} a^{4} \cdot 1^{0} : a^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} a^{3} \cdot 1^{1} : 4 a^{3}

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} a^{1} \cdot 1^{3} : 4 a

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} a^{0} \cdot 1^{4} : 1

= a^{4} + 4 a^{3} + 6 a^{2} + 4 a + 1

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Frequently Asked Questions (FAQ)

What is expand (a+1)^4 ?
The solution to expand (a+1)^4 is a^4+4a^3+6a^2+4a+1