What is expand (2x+7)^4 ?

The solution to expand (2x+7)^4 is 16x^4+224x^3+1176x^2+2744x+2401

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2x+7)^4

expand

(2 x + 7)^{4}

16 x^{4} + 224 x^{3} + 1176 x^{2} + 2744 x + 2401

Solution steps

(2 x + 7)^{4}

Apply binomial theorem:

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

a = 2 x, b = 7

= i = 0 \sum 4 (i 4) (2 x)^{(4 - i)} \cdot 7^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (2 x)^{4} \cdot 7^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (2 x)^{3} \cdot 7^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (2 x)^{2} \cdot 7^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (2 x)^{1} \cdot 7^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (2 x)^{0} \cdot 7^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 x)^{4} \cdot 7^{0} : 16 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 x)^{3} \cdot 7^{1} : 224 x^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 x)^{2} \cdot 7^{2} : 1176 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 x)^{1} \cdot 7^{3} : 2744 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 x)^{0} \cdot 7^{4} : 2401

= 16 x^{4} + 224 x^{3} + 1176 x^{2} + 2744 x + 2401

+ 36 m^{2} - 49 n^{2}

3320

\frac{3}{2}!

\frac{4}{5} \times \frac{5}{6}

27 - (- 12)

What is expand (2x+7)^4 ?
The solution to expand (2x+7)^4 is 16x^4+224x^3+1176x^2+2744x+2401