What is expand (2z-3k)^4 ?

The solution to expand (2z-3k)^4 is 16z^4-96z^3k+216z^2k^2-216zk^3+81k^4

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expand (2z-3k)^4

expand

(2 z - 3 k)^{4}

16 z^{4} - 96 z^{3} k + 216 z^{2} k^{2} - 216 z k^{3} + 81 k^{4}

Solution steps

(2 z - 3 k)^{4}

Apply binomial theorem:

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

a = 2 z, b = - 3 k

= i = 0 \sum 4 (i 4) (2 z)^{(4 - i)} (- 3 k)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 z)^{4} (- 3 k)^{0} : 16 z^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 z)^{3} (- 3 k)^{1} : - 96 z^{3} k

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 z)^{2} (- 3 k)^{2} : 216 z^{2} k^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 z)^{1} (- 3 k)^{3} : - 216 z k^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 z)^{0} (- 3 k)^{4} : 81 k^{4}

= 16 z^{4} - 96 z^{3} k + 216 z^{2} k^{2} - 216 z k^{3} + 81 k^{4}

\frac{x ^{n}}{x ^{n - 1}}

- 4 (- 3 t - 10 t - 7) - t

\frac{32}{60}

\frac{32}{64}

sin (x) - sin^{2} (x)

What is expand (2z-3k)^4 ?
The solution to expand (2z-3k)^4 is 16z^4-96z^3k+216z^2k^2-216zk^3+81k^4