What is expand (m+n)^4 ?

The solution to expand (m+n)^4 is m^4+4m^3n+6m^2n^2+4mn^3+n^4

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expand (m+n)^4

expand

(m + n)^{4}

m^{4} + 4 m^{3} n + 6 m^{2} n^{2} + 4 m n^{3} + n^{4}

Solution steps

(m + n)^{4}

Apply binomial theorem:

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

a = m, b = n

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} m^{2} n^{2} : 6 m^{2} n^{2}

Simplify

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

Simplify

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

= m^{4} + 4 m^{3} n + 6 m^{2} n^{2} + 4 m n^{3} + n^{4}

\frac{z ^{3} - 8}{z ^{2} + 2 z + 4}

\frac{4}{3} - \frac{5}{9}

\frac{4}{7} \cdot \frac{1}{2}

\frac{9}{2} \cdot \frac{5}{9}

\frac{( 9 - x ^{- 2} )}{3 + x ^{- 1}}

What is expand (m+n)^4 ?
The solution to expand (m+n)^4 is m^4+4m^3n+6m^2n^2+4mn^3+n^4