What is expand (4x-3)^5 ?

The solution to expand (4x-3)^5 is 1024x^5-3840x^4+5760x^3-4320x^2+1620x-243

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (4x-3)^5

expand

(4 x - 3)^{5}

1024 x^{5} - 3840 x^{4} + 5760 x^{3} - 4320 x^{2} + 1620 x - 243

Solution steps

(4 x - 3)^{5}

Apply binomial theorem:

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

a = 4 x, b = - 3

= i = 0 \sum 5 (i 5) (4 x)^{(5 - i)} (- 3)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (4 x)^{5} (- 3)^{0} : 1024 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} (- 3)^{1} : - 3840 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (4 x)^{3} (- 3)^{2} : 5760 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (4 x)^{2} (- 3)^{3} : - 4320 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (4 x)^{1} (- 3)^{4} : 1620 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (4 x)^{0} (- 3)^{5} : - 243

= 1024 x^{5} - 3840 x^{4} + 5760 x^{3} - 4320 x^{2} + 1620 x - 243

\frac{1}{2} \cdot 2 \cdot 3

\frac{1}{3 c} - \frac{1}{3 d}

\frac{2 x ^{2} - 10 x}{4 x}

2 \frac{1}{2} \cdot 4

2.6

What is expand (4x-3)^5 ?
The solution to expand (4x-3)^5 is 1024x^5-3840x^4+5760x^3-4320x^2+1620x-243