What is expand (1+(ax)/3)^4 ?

The solution to expand (1+(ax)/3)^4 is 1+(4ax+2a^2x^2)/3+(4a^3x^3)/(27)+(a^4x^4)/(81)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1+(ax)/3)^4

expand

(1 + \frac{a x}{3})^{4}

1 + \frac{4 a x + 2 a ^{2} x ^{2}}{3} + \frac{4 a ^{3} x ^{3}}{27} + \frac{a ^{4} x ^{4}}{81}

Solution steps

(1 + \frac{a x}{3})^{4}

Apply binomial theorem:

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

a = 1, b = \frac{a x}{3}

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (\frac{a x}{3})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (\frac{a x}{3})^{0} : 1

Simplify

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

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (\frac{a x}{3})^{3} : \frac{4 a ^{3} x ^{3}}{27}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (\frac{a x}{3})^{4} : \frac{a ^{4} x ^{4}}{81}

= 1 + \frac{4 a x}{3} + \frac{2 a ^{2} x ^{2}}{3} + \frac{4 a ^{3} x ^{3}}{27} + \frac{a ^{4} x ^{4}}{81}

Join

1 + \frac{4 a x}{3} + \frac{2 a ^{2} x ^{2}}{3} + \frac{4 a ^{3} x ^{3}}{27} + \frac{a ^{4} x ^{4}}{81} : 1 + \frac{4 a x + 2 a ^{2} x ^{2}}{3} + \frac{4 a ^{3} x ^{3}}{27} + \frac{a ^{4} x ^{4}}{81}

= 1 + \frac{4 a x + 2 a ^{2} x ^{2}}{3} + \frac{4 a ^{3} x ^{3}}{27} + \frac{a ^{4} x ^{4}}{81}

\frac{3 + sin ( 2 x )}{( 3 + tan ( x ) ) ^{2}}

\frac{4}{π} (cos (3 t) - sin (5 t))

(- sec (t) tan (t) + sin (t))^{2}

t y^{''} (t) + (3 t - 1) y^{'} (t) - (4 t + 9) y

What is expand (1+(ax)/3)^4 ?
The solution to expand (1+(ax)/3)^4 is 1+(4ax+2a^2x^2)/3+(4a^3x^3)/(27)+(a^4x^4)/(81)