What is expand (r-t)^4 ?

The solution to expand (r-t)^4 is r^4-4r^3t+6r^2t^2-4rt^3+t^4

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expand (r-t)^4

expand

(r - t)^{4}

r^{4} - 4 r^{3} t + 6 r^{2} t^{2} - 4 r t^{3} + t^{4}

Solution steps

(r - t)^{4}

Apply binomial theorem:

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

a = r, b = - t

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} r^{2} (- t)^{2} : 6 r^{2} t^{2}

Simplify

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

Simplify

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

= r^{4} - 4 r^{3} t + 6 r^{2} t^{2} - 4 r t^{3} + t^{4}

\frac{5 x}{2} - x

6.02 \times 1 0^{23}

\frac{12}{26}

\frac{6 x ^{3} + 42 x ^{2}}{2 x ^{2} + 26 x + 84}

(a + 2 x)^{7}

What is expand (r-t)^4 ?
The solution to expand (r-t)^4 is r^4-4r^3t+6r^2t^2-4rt^3+t^4