Solve (x + 5)(x - 2) - (2x + 2)(x - 4) | 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

$$(x+5)(x-2)-(2x+2)(x-4)$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of $x+5$ by each term of $x-2$.

$$x^{2}-2x+5x-10-\left(2x+2\right)\left(x-4\right)$$

Combine $-2x$ and $5x$ to get $3x$.

$$x^{2}+3x-10-\left(2x+2\right)\left(x-4\right)$$

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

$$x^{2}+3x-10-\left(2x^{2}-8x+2x-8\right)$$

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

$$x^{2}+3x-10-\left(2x^{2}-6x-8\right)$$

To find the opposite of $2x^{2}-6x-8$, find the opposite of each term.

$$x^{2}+3x-10-2x^{2}-\left(-6x\right)-\left(-8\right)$$

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

$$x^{2}+3x-10-2x^{2}+6x-\left(-8\right)$$

The opposite of $-8$ is $8$.

$$x^{2}+3x-10-2x^{2}+6x+8$$

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

$$-x^{2}+3x-10+6x+8$$

Combine $3x$ and $6x$ to get $9x$.

$$-x^{2}+9x-10+8$$

Add $-10$ and $8$ to get $-2$.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of $x+5$ by each term of $x-2$.

$$x^{2}-2x+5x-10-\left(2x+2\right)\left(x-4\right)$$

Combine $-2x$ and $5x$ to get $3x$.

$$x^{2}+3x-10-\left(2x+2\right)\left(x-4\right)$$

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

$$x^{2}+3x-10-\left(2x^{2}-8x+2x-8\right)$$

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

$$x^{2}+3x-10-\left(2x^{2}-6x-8\right)$$

To find the opposite of $2x^{2}-6x-8$, find the opposite of each term.

$$x^{2}+3x-10-2x^{2}-\left(-6x\right)-\left(-8\right)$$

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

$$x^{2}+3x-10-2x^{2}+6x-\left(-8\right)$$

The opposite of $-8$ is $8$.

$$x^{2}+3x-10-2x^{2}+6x+8$$

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

$$-x^{2}+3x-10+6x+8$$

Combine $3x$ and $6x$ to get $9x$.

$$-x^{2}+9x-10+8$$

Add $-10$ and $8$ to get $-2$.

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