Solve (-x+2)(4+x)/-3(4-x)(x+3)

$$( - x + 2 ) ( 4 + x ) / - 3 ( 4 - x ) ( x + 3 )$$

Evaluate

$$-\frac{\left(2-x\right)\left(x+3\right)\left(16-x^{2}\right)}{3}$$

Solution Steps

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

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

Express \frac{4\left(-x\right)+\left(-x\right)x+8+2x}{-3}\left(4-x\right) as a single fraction.

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

Express \frac{\left(4\left(-x\right)+\left(-x\right)x+8+2x\right)\left(4-x\right)}{-3}\left(x+3\right) as a single fraction.

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

Apply the distributive property by multiplying each term of 4\left(-x\right)+\left(-x\right)x+8+2x by each term of 4-x.

$$\frac{\left(16\left(-x\right)-4\left(-x\right)x+4\left(-x\right)x-\left(-x\right)x^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Multiply -4 and -1 to get 4.

$$\frac{\left(16\left(-x\right)+4xx+4\left(-x\right)x-\left(-x\right)x^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Multiply x and x to get x^{2}.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x-\left(-x\right)x^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Multiply -1 and -1 to get 1.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x+xx^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x+x^{3}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Combine -8x and 8x to get 0.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x+x^{3}+32-2x^{2}\right)\left(x+3\right)}{-3}$$

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

$$\frac{\left(16\left(-x\right)+2x^{2}+4\left(-x\right)x+x^{3}+32\right)\left(x+3\right)}{-3}$$

Apply the distributive property by multiplying each term of 16\left(-x\right)+2x^{2}+4\left(-x\right)x+x^{3}+32 by each term of x+3.

$$\frac{16\left(-x\right)x+48\left(-x\right)+2x^{3}+6x^{2}+4\left(-x\right)x^{2}+12\left(-x\right)x+x^{4}+3x^{3}+32x+96}{-3}$$

Combine 16\left(-x\right)x and 12\left(-x\right)x to get 28\left(-x\right)x.

$$\frac{28\left(-x\right)x+48\left(-x\right)+2x^{3}+6x^{2}+4\left(-x\right)x^{2}+x^{4}+3x^{3}+32x+96}{-3}$$

Combine 2x^{3} and 3x^{3} to get 5x^{3}.

$$\frac{28\left(-x\right)x+48\left(-x\right)+5x^{3}+6x^{2}+4\left(-x\right)x^{2}+x^{4}+32x+96}{-3}$$

Multiply 28 and -1 to get -28.

$$\frac{-28xx+48\left(-1\right)x+5x^{3}+6x^{2}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

Multiply x and x to get x^{2}.

$$\frac{-28x^{2}+48\left(-1\right)x+5x^{3}+6x^{2}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

Multiply 48 and -1 to get -48.

$$\frac{-28x^{2}-48x+5x^{3}+6x^{2}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

Combine -28x^{2} and 6x^{2} to get -22x^{2}.

$$\frac{-22x^{2}-48x+5x^{3}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-22x^{2}-48x+5x^{3}+4\left(-1\right)x^{3}+x^{4}+32x+96}{-3}$$

Multiply 4 and -1 to get -4.

$$\frac{-22x^{2}-48x+5x^{3}-4x^{3}+x^{4}+32x+96}{-3}$$

Combine 5x^{3} and -4x^{3} to get x^{3}.

$$\frac{-22x^{2}-48x+x^{3}+x^{4}+32x+96}{-3}$$

Combine -48x and 32x to get -16x.

$$\frac{-22x^{2}-16x+x^{3}+x^{4}+96}{-3}$$

Expand

$$-\frac{x^{4}}{3}-\frac{x^{3}}{3}+\frac{22x^{2}}{3}+\frac{16x}{3}-32$$

Solution Steps

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

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

Express \frac{4\left(-x\right)+\left(-x\right)x+8+2x}{-3}\left(4-x\right) as a single fraction.

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

Express \frac{\left(4\left(-x\right)+\left(-x\right)x+8+2x\right)\left(4-x\right)}{-3}\left(x+3\right) as a single fraction.

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

Apply the distributive property by multiplying each term of 4\left(-x\right)+\left(-x\right)x+8+2x by each term of 4-x.

$$\frac{\left(16\left(-x\right)-4\left(-x\right)x+4\left(-x\right)x-\left(-x\right)x^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Multiply -4 and -1 to get 4.

$$\frac{\left(16\left(-x\right)+4xx+4\left(-x\right)x-\left(-x\right)x^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Multiply x and x to get x^{2}.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x-\left(-x\right)x^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Multiply -1 and -1 to get 1.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x+xx^{2}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x+x^{3}+32-8x+8x-2x^{2}\right)\left(x+3\right)}{-3}$$

Combine -8x and 8x to get 0.

$$\frac{\left(16\left(-x\right)+4x^{2}+4\left(-x\right)x+x^{3}+32-2x^{2}\right)\left(x+3\right)}{-3}$$

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

$$\frac{\left(16\left(-x\right)+2x^{2}+4\left(-x\right)x+x^{3}+32\right)\left(x+3\right)}{-3}$$

Apply the distributive property by multiplying each term of 16\left(-x\right)+2x^{2}+4\left(-x\right)x+x^{3}+32 by each term of x+3.

$$\frac{16\left(-x\right)x+48\left(-x\right)+2x^{3}+6x^{2}+4\left(-x\right)x^{2}+12\left(-x\right)x+x^{4}+3x^{3}+32x+96}{-3}$$

Combine 16\left(-x\right)x and 12\left(-x\right)x to get 28\left(-x\right)x.

$$\frac{28\left(-x\right)x+48\left(-x\right)+2x^{3}+6x^{2}+4\left(-x\right)x^{2}+x^{4}+3x^{3}+32x+96}{-3}$$

Combine 2x^{3} and 3x^{3} to get 5x^{3}.

$$\frac{28\left(-x\right)x+48\left(-x\right)+5x^{3}+6x^{2}+4\left(-x\right)x^{2}+x^{4}+32x+96}{-3}$$

Multiply 28 and -1 to get -28.

$$\frac{-28xx+48\left(-1\right)x+5x^{3}+6x^{2}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

Multiply x and x to get x^{2}.

$$\frac{-28x^{2}+48\left(-1\right)x+5x^{3}+6x^{2}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

Multiply 48 and -1 to get -48.

$$\frac{-28x^{2}-48x+5x^{3}+6x^{2}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

Combine -28x^{2} and 6x^{2} to get -22x^{2}.

$$\frac{-22x^{2}-48x+5x^{3}+4\left(-1\right)xx^{2}+x^{4}+32x+96}{-3}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-22x^{2}-48x+5x^{3}+4\left(-1\right)x^{3}+x^{4}+32x+96}{-3}$$

Multiply 4 and -1 to get -4.

$$\frac{-22x^{2}-48x+5x^{3}-4x^{3}+x^{4}+32x+96}{-3}$$

Combine 5x^{3} and -4x^{3} to get x^{3}.

$$\frac{-22x^{2}-48x+x^{3}+x^{4}+32x+96}{-3}$$

Combine -48x and 32x to get -16x.

$$\frac{-22x^{2}-16x+x^{3}+x^{4}+96}{-3}$$