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Popular >

expand (d+1)^4

Solution

expand

(d + 1)^{4}

Solution

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

Solution steps

(d + 1)^{4}

Apply binomial theorem:

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

a = d, b = 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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