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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2-3x)^4

expand

(2 - 3 x)^{4}

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

Solution steps

(2 - 3 x)^{4}

Apply binomial theorem:

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

a = 2, b = - 3 x

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{1}{5} - \frac{9}{64}

y^{2} - 13 y + 12

0.064

\frac{\frac{2}{9}}{\frac{1}{3}}

4^{l o g_{10} (n^{2})}

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