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Popular >

expand (s+2)^4

Solution

expand

(s + 2)^{4}

Solution

s^{4} + 8 s^{3} + 24 s^{2} + 32 s + 16

Solution steps

(s + 2)^{4}

Apply binomial theorem:

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

a = s, b = 2

= i = 0 \sum 4 (i 4) s^{(4 - i)} \cdot 2^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} s^{4} \cdot 2^{0} : s^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} s^{3} \cdot 2^{1} : 8 s^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} s^{2} \cdot 2^{2} : 24 s^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} s^{1} \cdot 2^{3} : 32 s

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} s^{0} \cdot 2^{4} : 16

= s^{4} + 8 s^{3} + 24 s^{2} + 32 s + 16

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Frequently Asked Questions (FAQ)

What is expand (s+2)^4 ?
The solution to expand (s+2)^4 is s^4+8s^3+24s^2+32s+16