Solve (3x+2)(x+y-z)-(3x+2)-(x+y-1)(3x+2) | 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

$$(3x+2)(x+y-z)-(3x+2)-(x+y-1)(3x+2)$$

Evaluate

$z\left(-3x-2\right)$

Solution Steps

Apply the distributive property by multiplying each term of $3x+2$ by each term of $x+y-z$.

$$3x^{2}+3xy-3xz+2x+2y-2z-\left(3x+2\right)-\left(x+y-1\right)\left(3x+2\right)$$

To find the opposite of $3x+2$, find the opposite of each term.

$$3x^{2}+3xy-3xz+2x+2y-2z-3x-2-\left(x+y-1\right)\left(3x+2\right)$$

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

$$3x^{2}+3xy-3xz-x+2y-2z-2-\left(x+y-1\right)\left(3x+2\right)$$

Apply the distributive property by multiplying each term of $x+y-1$ by each term of $3x+2$.

$$3x^{2}+3xy-3xz-x+2y-2z-2-\left(3x^{2}+2x+3yx+2y-3x-2\right)$$

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

$$3x^{2}+3xy-3xz-x+2y-2z-2-\left(3x^{2}-x+3yx+2y-2\right)$$

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

$$3x^{2}+3xy-3xz-x+2y-2z-2-3x^{2}-\left(-x\right)-3yx-2y-\left(-2\right)$$

The opposite of $-x$ is $x$.

$$3x^{2}+3xy-3xz-x+2y-2z-2-3x^{2}+x-3yx-2y-\left(-2\right)$$

The opposite of $-2$ is $2$.

$$3x^{2}+3xy-3xz-x+2y-2z-2-3x^{2}+x-3yx-2y+2$$

Combine $3x^{2}$ and $-3x^{2}$ to get $0$.

$$3xy-3xz-x+2y-2z-2+x-3yx-2y+2$$

Combine $-x$ and $x$ to get $0$.

$$3xy-3xz+2y-2z-2-3yx-2y+2$$

Combine $3xy$ and $-3yx$ to get $0$.

$$-3xz+2y-2z-2-2y+2$$

Combine $2y$ and $-2y$ to get $0$.

$$-3xz-2z-2+2$$

Add $-2$ and $2$ to get $0$.

$$-3xz-2z$$

Expand

$-3xz-2z$

Solution Steps

Apply the distributive property by multiplying each term of $3x+2$ by each term of $x+y-z$.

$$3x^{2}+3xy-3xz+2x+2y-2z-\left(3x+2\right)-\left(x+y-1\right)\left(3x+2\right)$$

To find the opposite of $3x+2$, find the opposite of each term.

$$3x^{2}+3xy-3xz+2x+2y-2z-3x-2-\left(x+y-1\right)\left(3x+2\right)$$

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

$$3x^{2}+3xy-3xz-x+2y-2z-2-\left(x+y-1\right)\left(3x+2\right)$$

Apply the distributive property by multiplying each term of $x+y-1$ by each term of $3x+2$.

$$3x^{2}+3xy-3xz-x+2y-2z-2-\left(3x^{2}+2x+3yx+2y-3x-2\right)$$

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

$$3x^{2}+3xy-3xz-x+2y-2z-2-\left(3x^{2}-x+3yx+2y-2\right)$$

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

$$3x^{2}+3xy-3xz-x+2y-2z-2-3x^{2}-\left(-x\right)-3yx-2y-\left(-2\right)$$

The opposite of $-x$ is $x$.

$$3x^{2}+3xy-3xz-x+2y-2z-2-3x^{2}+x-3yx-2y-\left(-2\right)$$

The opposite of $-2$ is $2$.

$$3x^{2}+3xy-3xz-x+2y-2z-2-3x^{2}+x-3yx-2y+2$$

Combine $3x^{2}$ and $-3x^{2}$ to get $0$.

$$3xy-3xz-x+2y-2z-2+x-3yx-2y+2$$

Combine $-x$ and $x$ to get $0$.

$$3xy-3xz+2y-2z-2-3yx-2y+2$$

Combine $3xy$ and $-3yx$ to get $0$.

$$-3xz+2y-2z-2-2y+2$$

Combine $2y$ and $-2y$ to get $0$.

$$-3xz-2z-2+2$$

Add $-2$ and $2$ to get $0$.

$$-3xz-2z$$