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

The solution to expand (x-1)^2(x+2)^3 is x^5+4x^4+x^3-10x^2-4x+8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

expand

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

x^{5} + 4 x^{4} + x^{3} - 10 x^{2} - 4 x + 8

Solution steps

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

Expand

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

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

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

Expand

(x + 2)^{3} : x^{3} + 6 x^{2} + 12 x + 8

= (x^{3} + 6 x^{2} + 12 x + 8) (x^{2} - 2 x + 1)

Distribute parentheses

= x^{3} x^{2} + x^{3} (- 2 x) + x^{3} \cdot 1 + 6 x^{2} x^{2} + 6 x^{2} (- 2 x) + 6 x^{2} \cdot 1 + 12 x x^{2} + 12 x (- 2 x) + 12 x \cdot 1 + 8 x^{2} + 8 (- 2 x) + 8 \cdot 1

Simplify

x^{3} x^{2} + x^{3} (- 2 x) + x^{3} \cdot 1 + 6 x^{2} x^{2} + 6 x^{2} (- 2 x) + 6 x^{2} \cdot 1 + 12 x x^{2} + 12 x (- 2 x) + 12 x \cdot 1 + 8 x^{2} + 8 (- 2 x) + 8 \cdot 1 : x^{5} + 4 x^{4} + x^{3} - 10 x^{2} - 4 x + 8

= x^{5} + 4 x^{4} + x^{3} - 10 x^{2} - 4 x + 8

- 4 + \frac{5}{2}

\frac{x ^{2} - 3 x - 4}{x ^{2} - 12 x + 32}

\frac{7 x}{7 x + 4}

\frac{3 x - 10}{x - 1} - \frac{5 x - 12}{x - 1}

14

What is expand (x-1)^2(x+2)^3 ?
The solution to expand (x-1)^2(x+2)^3 is x^5+4x^4+x^3-10x^2-4x+8