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

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

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

simplify

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

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

Solution steps

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

Apply FOIL method

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

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

Expand

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

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

Distribute parentheses

= 1 + 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

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

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

32 \cdot \frac{1}{2}

(4 x^{2} - 2 x y + 5) - (x^{2} + x y - 1)

\frac{x ^{2}}{x ^{- 1}}

\frac{9}{121}

\frac{1}{15} + \frac{8}{9}

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