Solve x(x+1)(x+2)(x+3)/x(x+1) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x(x+1)(x+2)(x+3)/x(x+1)$$

Evaluate

$\left(x+2\right)\left(x+3\right)\left(x+1\right)^{2}$

Solution Steps

Cancel out $x$ in both numerator and denominator.

$$\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of $x+1$ by each term of $x+2$.

$$\left(x^{2}+2x+x+2\right)\left(x+3\right)\left(x+1\right)$$

Combine $2x$ and $x$ to get $3x$.

$$\left(x^{2}+3x+2\right)\left(x+3\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of $x^{2}+3x+2$ by each term of $x+3$.

$$\left(x^{3}+3x^{2}+3x^{2}+9x+2x+6\right)\left(x+1\right)$$

Combine $3x^{2}$ and $3x^{2}$ to get $6x^{2}$.

$$\left(x^{3}+6x^{2}+9x+2x+6\right)\left(x+1\right)$$

Combine $9x$ and $2x$ to get $11x$.

$$\left(x^{3}+6x^{2}+11x+6\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of $x^{3}+6x^{2}+11x+6$ by each term of $x+1$.

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

Combine $x^{3}$ and $6x^{3}$ to get $7x^{3}$.

$$x^{4}+7x^{3}+6x^{2}+11x^{2}+11x+6x+6$$

Combine $6x^{2}$ and $11x^{2}$ to get $17x^{2}$.

$$x^{4}+7x^{3}+17x^{2}+11x+6x+6$$

Combine $11x$ and $6x$ to get $17x$.

$$x^{4}+7x^{3}+17x^{2}+17x+6$$

Expand

$x^{4}+7x^{3}+17x^{2}+17x+6$

Solution Steps

Cancel out $x$ in both numerator and denominator.

$$\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of $x+1$ by each term of $x+2$.

$$\left(x^{2}+2x+x+2\right)\left(x+3\right)\left(x+1\right)$$

Combine $2x$ and $x$ to get $3x$.

$$\left(x^{2}+3x+2\right)\left(x+3\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of $x^{2}+3x+2$ by each term of $x+3$.

$$\left(x^{3}+3x^{2}+3x^{2}+9x+2x+6\right)\left(x+1\right)$$

Combine $3x^{2}$ and $3x^{2}$ to get $6x^{2}$.

$$\left(x^{3}+6x^{2}+9x+2x+6\right)\left(x+1\right)$$

Combine $9x$ and $2x$ to get $11x$.

$$\left(x^{3}+6x^{2}+11x+6\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of $x^{3}+6x^{2}+11x+6$ by each term of $x+1$.

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

Combine $x^{3}$ and $6x^{3}$ to get $7x^{3}$.

$$x^{4}+7x^{3}+6x^{2}+11x^{2}+11x+6x+6$$

Combine $6x^{2}$ and $11x^{2}$ to get $17x^{2}$.

$$x^{4}+7x^{3}+17x^{2}+11x+6x+6$$

Combine $11x$ and $6x$ to get $17x$.

$$x^{4}+7x^{3}+17x^{2}+17x+6$$