What is sqrt(x(x+1)(x+2)(x+3)+1) ?

The solution to sqrt(x(x+1)(x+2)(x+3)+1) is sqrt(x^4+6x^3+11x^2+6x+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt(x(x+1)(x+2)(x+3)+1)

simplify

x (x + 1) (x + 2) (x + 3) + 1

x^{4} + 6 x^{3} + 11 x^{2} + 6 x + 1

Solution steps

x (x + 1) (x + 2) (x + 3) + 1

Apply FOIL method

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

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

Expand

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

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

Distribute parentheses

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

Simplify

x^{2} x^{2} + x^{2} \cdot 3 x + x^{2} \cdot 2 + 3 x x^{2} + 3 x \cdot 3 x + 3 x \cdot 2 : x^{4} + 6 x^{3} + 11 x^{2} + 6 x

= x^{4} + 6 x^{3} + 11 x^{2} + 6 x + 1

(x - 3) (x + 3)

(x - 2) (x + 2)

(2 + 3 z + z^{2})^{5}

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

tan^{2} (a) (2 cos^{2} (a) + sin^{2} (a) - 1)

What is sqrt(x(x+1)(x+2)(x+3)+1) ?
The solution to sqrt(x(x+1)(x+2)(x+3)+1) is sqrt(x^4+6x^3+11x^2+6x+1)