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Popular >

expand (2+h)^4

Solution

expand

(2 + h)^{4}

Solution

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

Solution steps

(2 + h)^{4}

Apply binomial theorem:

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

a = 2, b = h

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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