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

The solution to expand (z-3x)^4 is z^4-12z^3x+54z^2x^2-108zx^3+81x^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (z-3x)^4

expand

(z - 3 x)^{4}

z^{4} - 12 z^{3} x + 54 z^{2} x^{2} - 108 z x^{3} + 81 x^{4}

Solution steps

(z - 3 x)^{4}

Apply binomial theorem:

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

a = z, b = - 3 x

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} z^{3} (- 3 x)^{1} : - 12 z^{3} x

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} z^{2} (- 3 x)^{2} : 54 z^{2} x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} z^{1} (- 3 x)^{3} : - 108 z x^{3}

Simplify

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

= z^{4} - 12 z^{3} x + 54 z^{2} x^{2} - 108 z x^{3} + 81 x^{4}

2 x^{3} \times 2 x^{2}

4.95 \cdot 0.5 + 5 \cdot 0.01

\frac{3 ^{2}}{4 ^{2}}

2^{40.2}

\frac{5 x}{6} + \frac{x}{5}

What is expand (z-3x)^4 ?
The solution to expand (z-3x)^4 is z^4-12z^3x+54z^2x^2-108zx^3+81x^4