What is expand (m+j)^4 ?

The solution to expand (m+j)^4 is m^4+4jm^3+6j^2m^2+4j^3m+j^4

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expand (m+j)^4

expand

(m + j)^{4}

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

Solution steps

(m + j)^{4}

Apply binomial theorem:

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

a = m, b = j

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(6) (9)

\frac{6 π}{7 π}

1 0^{2} - 7^{2}

\frac{a}{8 - a}

6 x^{2} + 23 x - 4

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