What is expand (3-2x)^5 ?

The solution to expand (3-2x)^5 is 243-810x+1080x^2-720x^3+240x^4-32x^5

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expand (3-2x)^5

expand

(3 - 2 x)^{5}

243 - 810 x + 1080 x^{2} - 720 x^{3} + 240 x^{4} - 32 x^{5}

Solution steps

(3 - 2 x)^{5}

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 5 (i 5) \cdot 3^{(5 - i)} (- 2 x)^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (- 2 x)^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (- 2 x)^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (- 2 x)^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (- 2 x)^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (- 2 x)^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (- 2 x)^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 3^{5} (- 2 x)^{0} : 243

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 3^{4} (- 2 x)^{1} : - 810 x

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 3^{3} (- 2 x)^{2} : 1080 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 3^{2} (- 2 x)^{3} : - 720 x^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 3^{1} (- 2 x)^{4} : 240 x^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 3^{0} (- 2 x)^{5} : - 32 x^{5}

= 243 - 810 x + 1080 x^{2} - 720 x^{3} + 240 x^{4} - 32 x^{5}

0.3 a + 0.4 b + 0.5 c - 0.6 a - 0.7 b - 0.9 c + 3 a - 3 b - 3 c

- 10 - 9

- 15 - 8

\frac{x - 2}{x ^{2} - 4 x + 4}

\frac{5}{8} \cdot \frac{1}{2}

What is expand (3-2x)^5 ?
The solution to expand (3-2x)^5 is 243-810x+1080x^2-720x^3+240x^4-32x^5