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

The solution to expand (1+2x-3x^2+x^3)^2 is x^6-6x^5+13x^4-10x^3-2x^2+4x+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

expand

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

x^{6} - 6 x^{5} + 13 x^{4} - 10 x^{3} - 2 x^{2} + 4 x + 1

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Distribute parentheses

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

Simplify

1 \cdot 1 + 1 \cdot 2 x + 1 \cdot (- 3 x^{2}) + 1 \cdot x^{3} + 2 x \cdot 1 + 2 x \cdot 2 x + 2 x (- 3 x^{2}) + 2 x x^{3} - 3 x^{2} \cdot 1 - 3 x^{2} \cdot 2 x - 3 x^{2} (- 3 x^{2}) - 3 x^{2} x^{3} + x^{3} \cdot 1 + x^{3} \cdot 2 x + x^{3} (- 3 x^{2}) + x^{3} x^{3} : x^{6} - 6 x^{5} + 13 x^{4} - 10 x^{3} - 2 x^{2} + 4 x + 1

= x^{6} - 6 x^{5} + 13 x^{4} - 10 x^{3} - 2 x^{2} + 4 x + 1

5 \times 0

9 \times 9 \times 9 \times 9

7 \times (- 3)

x y + 9 x - 3 y - 27

What is expand (1+2x-3x^2+x^3)^2 ?
The solution to expand (1+2x-3x^2+x^3)^2 is x^6-6x^5+13x^4-10x^3-2x^2+4x+1