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

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

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simplify 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

\frac{3}{8} \cdot \frac{1}{2}

(13 + - 180) (6 + - 180)

(3 cos (t))^{2}

\frac{64}{5}

\frac{a ^{2} - 5 a + 6}{3 a - 15} \cdot \frac{6 a}{a ^{2} - a - 30} \cdot \frac{a ^{2} - 25}{2 a - 4}

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