What is expand (4r+t)^4 ?

The solution to expand (4r+t)^4 is 256r^4+256r^3t+96r^2t^2+16rt^3+t^4

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expand (4r+t)^4

expand

(4 r + t)^{4}

256 r^{4} + 256 r^{3} t + 96 r^{2} t^{2} + 16 r t^{3} + t^{4}

Solution steps

(4 r + t)^{4}

Apply binomial theorem:

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

a = 4 r, b = t

= i = 0 \sum 4 (i 4) (4 r)^{(4 - i)} t^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (4 r)^{4} t^{0} : 256 r^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (4 r)^{3} t^{1} : 256 r^{3} t

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (4 r)^{2} t^{2} : 96 r^{2} t^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (4 r)^{1} t^{3} : 16 r t^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (4 r)^{0} t^{4} : t^{4}

= 256 r^{4} + 256 r^{3} t + 96 r^{2} t^{2} + 16 r t^{3} + t^{4}

4 - \frac{7}{6}

\frac{1}{10} \div 2

x^{2} y^{3} + y^{4}

\frac{- 18}{12}

- 4 \frac{2}{3}

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