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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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}

- 1 \div \frac{1}{4}

- 7^{6}

\frac{7}{8} \times \frac{5}{6}

e^{l n (2) - l n (3)}

x^{2} + 10 x - 75

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