What is expand (2a+5)^4 ?

The solution to expand (2a+5)^4 is 16a^4+160a^3+600a^2+1000a+625

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2a+5)^4

expand

(2 a + 5)^{4}

16 a^{4} + 160 a^{3} + 600 a^{2} + 1000 a + 625

Solution steps

(2 a + 5)^{4}

Apply binomial theorem:

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

a = 2 a, b = 5

= i = 0 \sum 4 (i 4) (2 a)^{(4 - i)} \cdot 5^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 a)^{4} \cdot 5^{0} : 16 a^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 a)^{3} \cdot 5^{1} : 160 a^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 a)^{2} \cdot 5^{2} : 600 a^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 a)^{1} \cdot 5^{3} : 1000 a

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 a)^{0} \cdot 5^{4} : 625

= 16 a^{4} + 160 a^{3} + 600 a^{2} + 1000 a + 625

- 3 x^{2} + 2 x^{2}

9 + (- 9)

3 \times (- 7)

(x - y) (2 x - y)

What is expand (2a+5)^4 ?
The solution to expand (2a+5)^4 is 16a^4+160a^3+600a^2+1000a+625