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Popular >

expand (m+4)^4

Solution

expand

(m + 4)^{4}

Solution

m^{4} + 16 m^{3} + 96 m^{2} + 256 m + 256

Solution steps

(m + 4)^{4}

Apply binomial theorem:

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

a = m, b = 4

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} m^{3} \cdot 4^{1} : 16 m^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} m^{2} \cdot 4^{2} : 96 m^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} m^{1} \cdot 4^{3} : 256 m

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} m^{0} \cdot 4^{4} : 256

= m^{4} + 16 m^{3} + 96 m^{2} + 256 m + 256

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Frequently Asked Questions (FAQ)

What is expand (m+4)^4 ?
The solution to expand (m+4)^4 is m^4+16m^3+96m^2+256m+256