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

The solution to expand (3-3z)^4 is 81-324z+486z^2-324z^3+81z^4

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expand (3-3z)^4

expand

(3 - 3 z)^{4}

81 - 324 z + 486 z^{2} - 324 z^{3} + 81 z^{4}

Solution steps

(3 - 3 z)^{4}

Apply binomial theorem:

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

a = 3, b = - 3 z

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 3^{3} (- 3 z)^{1} : - 324 z

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 3^{2} (- 3 z)^{2} : 486 z^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 3^{1} (- 3 z)^{3} : - 324 z^{3}

Simplify

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

= 81 - 324 z + 486 z^{2} - 324 z^{3} + 81 z^{4}

- x^{3} 20 - 3 x^{2} 5 x^{2}

x^{3} - 8 x^{2} - x + 8

- 6 (- \frac{x}{6})

\frac{1}{1 ^{3}}

5 x + 2 - 4 x + 3

What is expand (3-3z)^4 ?
The solution to expand (3-3z)^4 is 81-324z+486z^2-324z^3+81z^4