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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2x+3)^4

expand

(2 x + 3)^{4}

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

Solution steps

(2 x + 3)^{4}

Apply binomial theorem:

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

a = 2 x, b = 3

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{\frac{1}{x}}{x}

\frac{21}{5}

(a + b + c) (a + b - c)

- 1 \times 1

3 x \cdot 2 x

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