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

$$-(x-3)(3x+1)-(2x-6)(x+1)}{1-x}$$

Evaluate

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

Solution Steps

To find the opposite of $x-3$, find the opposite of each term.

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

The opposite of $-3$ is $3$.

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

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

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

Combine $-x$ and $9x$ to get $8x$.

$$-3x^{2}+8x+3-\left(2x-6\right)\left(x+1\right)\left(1-x\right)$$

Apply the distributive property by multiplying each term of $2x-6$ by each term of $x+1$.

$$-3x^{2}+8x+3-\left(2x^{2}+2x-6x-6\right)\left(1-x\right)$$

Combine $2x$ and $-6x$ to get $-4x$.

$$-3x^{2}+8x+3-\left(2x^{2}-4x-6\right)\left(1-x\right)$$

Apply the distributive property by multiplying each term of $2x^{2}-4x-6$ by each term of $1-x$.

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

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

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

Combine $-4x$ and $6x$ to get $2x$.

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

To find the opposite of $6x^{2}-2x^{3}+2x-6$, find the opposite of each term.

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

The opposite of $-2x^{3}$ is $2x^{3}$.

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

The opposite of $-6$ is $6$.

$$-3x^{2}+8x+3-6x^{2}+2x^{3}-2x+6$$

Combine $-3x^{2}$ and $-6x^{2}$ to get $-9x^{2}$.

$$-9x^{2}+8x+3+2x^{3}-2x+6$$

Combine $8x$ and $-2x$ to get $6x$.

$$-9x^{2}+6x+3+2x^{3}+6$$

Add $3$ and $6$ to get $9$.

$$-9x^{2}+6x+9+2x^{3}$$

Expand

$2x^{3}-9x^{2}+6x+9$

Solution Steps

To find the opposite of $x-3$, find the opposite of each term.

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

The opposite of $-3$ is $3$.

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

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

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

Combine $-x$ and $9x$ to get $8x$.

$$-3x^{2}+8x+3-\left(2x-6\right)\left(x+1\right)\left(1-x\right)$$

Apply the distributive property by multiplying each term of $2x-6$ by each term of $x+1$.

$$-3x^{2}+8x+3-\left(2x^{2}+2x-6x-6\right)\left(1-x\right)$$

Combine $2x$ and $-6x$ to get $-4x$.

$$-3x^{2}+8x+3-\left(2x^{2}-4x-6\right)\left(1-x\right)$$

Apply the distributive property by multiplying each term of $2x^{2}-4x-6$ by each term of $1-x$.

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

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

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

Combine $-4x$ and $6x$ to get $2x$.

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

To find the opposite of $6x^{2}-2x^{3}+2x-6$, find the opposite of each term.

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

The opposite of $-2x^{3}$ is $2x^{3}$.

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

The opposite of $-6$ is $6$.

$$-3x^{2}+8x+3-6x^{2}+2x^{3}-2x+6$$

Combine $-3x^{2}$ and $-6x^{2}$ to get $-9x^{2}$.

$$-9x^{2}+8x+3+2x^{3}-2x+6$$

Combine $8x$ and $-2x$ to get $6x$.

$$-9x^{2}+6x+3+2x^{3}+6$$

Add $3$ and $6$ to get $9$.

$$-9x^{2}+6x+9+2x^{3}$$