What is expand (x-1)^3(x+1)(x+1/2) ?

The solution to expand (x-1)^3(x+1)(x+1/2) is x^5-(3x^4)/2+2x^2-x^3-1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x-1)^3(x+1)(x+1/2)

expand

(x - 1)^{3} (x + 1) (x + \frac{1}{2})

x^{5} - \frac{3 x ^{4}}{2} + 2 x^{2} - x^{3} - \frac{1}{2}

Solution steps

(x - 1)^{3} (x + 1) (x + \frac{1}{2})

Expand

(x - 1)^{3} : x^{3} - 3 x^{2} + 3 x - 1

= (x^{3} - 3 x^{2} + 3 x - 1) (x + 1) (x + \frac{1}{2})

Apply FOIL method

(x + 1) (x + \frac{1}{2}) : x^{2} + \frac{3 x}{2} + \frac{1}{2}

= (x^{3} - 3 x^{2} + 3 x - 1) (x^{2} + \frac{3 x}{2} + \frac{1}{2})

Distribute parentheses

= x^{3} x^{2} + x^{3} \frac{3 x}{2} + x^{3} \frac{1}{2} - 3 x^{2} x^{2} - 3 x^{2} \frac{3 x}{2} - 3 x^{2} \frac{1}{2} + 3 x x^{2} + 3 x \frac{3 x}{2} + 3 x \frac{1}{2} - 1 \cdot x^{2} - 1 \cdot \frac{3 x}{2} - 1 \cdot \frac{1}{2}

Simplify

x^{3} x^{2} + x^{3} \frac{3 x}{2} + x^{3} \frac{1}{2} - 3 x^{2} x^{2} - 3 x^{2} \frac{3 x}{2} - 3 x^{2} \frac{1}{2} + 3 x x^{2} + 3 x \frac{3 x}{2} + 3 x \frac{1}{2} - 1 \cdot x^{2} - 1 \cdot \frac{3 x}{2} - 1 \cdot \frac{1}{2} : x^{5} - \frac{3 x ^{4}}{2} + 2 x^{2} - x^{3} - \frac{1}{2}

= x^{5} - \frac{3 x ^{4}}{2} + 2 x^{2} - x^{3} - \frac{1}{2}

e^{2 t} (cos (2 x) - sin (2 x))

2 (2 x^{2} + y^{2}) d x - x y d y

(x + 2 π)^{4}

- (\frac{8 x}{y} - \frac{w}{t})^{2}

What is expand (x-1)^3(x+1)(x+1/2) ?
The solution to expand (x-1)^3(x+1)(x+1/2) is x^5-(3x^4)/2+2x^2-x^3-1/2