What is expand (3-2x)^4 ?

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

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expand (3-2x)^4

expand

(3 - 2 x)^{4}

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

Solution steps

(3 - 2 x)^{4}

Apply binomial theorem:

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

a = 3, b = - 2 x

= i = 0 \sum 4 (i 4) \cdot 3^{(4 - i)} (- 2 x)^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 3^{4} (- 2 x)^{0} : 81

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 3^{3} (- 2 x)^{1} : - 216 x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 3^{2} (- 2 x)^{2} : 216 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 3^{1} (- 2 x)^{3} : - 96 x^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 3^{0} (- 2 x)^{4} : 16 x^{4}

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

4 - - 1 + 64 - - 9

120000

\frac{x + y}{x - y} - \frac{x - y}{x + y}

\frac{x + 3}{6} - \frac{x - 2}{30}

612 - 123 + 100

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