Solve (x+1)(x+3)(x-2)(x-6)+96 | 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

$$(x+1)(x+3)(x-2)(x-6)+96$$

Evaluate

$\left(x-6\right)\left(x-2\right)\left(x+1\right)\left(x+3\right)+96$

Solution Steps

Apply the distributive property by multiplying each term of $x+1$ by each term of $x+3$.

$$\left(x^{2}+3x+x+3\right)\left(x-2\right)\left(x-6\right)+96$$

Combine $3x$ and $x$ to get $4x$.

$$\left(x^{2}+4x+3\right)\left(x-2\right)\left(x-6\right)+96$$

Apply the distributive property by multiplying each term of $x^{2}+4x+3$ by each term of $x-2$.

$$\left(x^{3}-2x^{2}+4x^{2}-8x+3x-6\right)\left(x-6\right)+96$$

Combine $-2x^{2}$ and $4x^{2}$ to get $2x^{2}$.

$$\left(x^{3}+2x^{2}-8x+3x-6\right)\left(x-6\right)+96$$

Combine $-8x$ and $3x$ to get $-5x$.

$$\left(x^{3}+2x^{2}-5x-6\right)\left(x-6\right)+96$$

Apply the distributive property by multiplying each term of $x^{3}+2x^{2}-5x-6$ by each term of $x-6$.

$$x^{4}-6x^{3}+2x^{3}-12x^{2}-5x^{2}+30x-6x+36+96$$

Combine $-6x^{3}$ and $2x^{3}$ to get $-4x^{3}$.

$$x^{4}-4x^{3}-12x^{2}-5x^{2}+30x-6x+36+96$$

Combine $-12x^{2}$ and $-5x^{2}$ to get $-17x^{2}$.

$$x^{4}-4x^{3}-17x^{2}+30x-6x+36+96$$

Combine $30x$ and $-6x$ to get $24x$.

$$x^{4}-4x^{3}-17x^{2}+24x+36+96$$

Add $36$ and $96$ to get $132$.

$$x^{4}-4x^{3}-17x^{2}+24x+132$$

Expand

$x^{4}-4x^{3}-17x^{2}+24x+132$

Solution Steps

Apply the distributive property by multiplying each term of $x+1$ by each term of $x+3$.

$$\left(x^{2}+3x+x+3\right)\left(x-2\right)\left(x-6\right)+96$$

Combine $3x$ and $x$ to get $4x$.

$$\left(x^{2}+4x+3\right)\left(x-2\right)\left(x-6\right)+96$$

Apply the distributive property by multiplying each term of $x^{2}+4x+3$ by each term of $x-2$.

$$\left(x^{3}-2x^{2}+4x^{2}-8x+3x-6\right)\left(x-6\right)+96$$

Combine $-2x^{2}$ and $4x^{2}$ to get $2x^{2}$.

$$\left(x^{3}+2x^{2}-8x+3x-6\right)\left(x-6\right)+96$$

Combine $-8x$ and $3x$ to get $-5x$.

$$\left(x^{3}+2x^{2}-5x-6\right)\left(x-6\right)+96$$

Apply the distributive property by multiplying each term of $x^{3}+2x^{2}-5x-6$ by each term of $x-6$.

$$x^{4}-6x^{3}+2x^{3}-12x^{2}-5x^{2}+30x-6x+36+96$$

Combine $-6x^{3}$ and $2x^{3}$ to get $-4x^{3}$.

$$x^{4}-4x^{3}-12x^{2}-5x^{2}+30x-6x+36+96$$

Combine $-12x^{2}$ and $-5x^{2}$ to get $-17x^{2}$.

$$x^{4}-4x^{3}-17x^{2}+30x-6x+36+96$$

Combine $30x$ and $-6x$ to get $24x$.

$$x^{4}-4x^{3}-17x^{2}+24x+36+96$$

Add $36$ and $96$ to get $132$.

$$x^{4}-4x^{3}-17x^{2}+24x+132$$