What is expand (1/2-3a)^4 ?

The solution to expand (1/2-3a)^4 is 1/16-(3a)/2+(27a^2)/2-54a^3+81a^4

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expand (1/2-3a)^4

expand

(\frac{1}{2} - 3 a)^{4}

\frac{1}{16} - \frac{3 a}{2} + \frac{27 a ^{2}}{2} - 54 a^{3} + 81 a^{4}

Solution steps

(\frac{1}{2} - 3 a)^{4}

Apply binomial theorem:

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

a = \frac{1}{2}, b = - 3 a

= i = 0 \sum 4 (i 4) (\frac{1}{2})^{(4 - i)} (- 3 a)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (\frac{1}{2})^{4} (- 3 a)^{0} : \frac{1}{16}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (\frac{1}{2})^{3} (- 3 a)^{1} : - \frac{3 a}{2}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (\frac{1}{2})^{2} (- 3 a)^{2} : \frac{27 a ^{2}}{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (\frac{1}{2})^{1} (- 3 a)^{3} : - 54 a^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (\frac{1}{2})^{0} (- 3 a)^{4} : 81 a^{4}

= \frac{1}{16} - \frac{3 a}{2} + \frac{27 a ^{2}}{2} - 54 a^{3} + 81 a^{4}

- ∣ 15 ∣

16 x^{2} - 8 x + 1

- 0.8 (3 x - 31) + 5.5

a^{2} - 6 a - 7

(- 17)^{2}

What is expand (1/2-3a)^4 ?
The solution to expand (1/2-3a)^4 is 1/16-(3a)/2+(27a^2)/2-54a^3+81a^4