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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of 4x+3.

$$\left(4x^{2}+3x-12x-9\right)\left(2+x\right)\left(x-2\right)$$

Combine 3x and -12x to get -9x.

$$\left(4x^{2}-9x-9\right)\left(2+x\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 4x^{2}-9x-9 by each term of 2+x.

$$\left(8x^{2}+4x^{3}-18x-9x^{2}-18-9x\right)\left(x-2\right)$$

Combine 8x^{2} and -9x^{2} to get -x^{2}.

$$\left(-x^{2}+4x^{3}-18x-18-9x\right)\left(x-2\right)$$

Combine -18x and -9x to get -27x.

$$\left(-x^{2}+4x^{3}-27x-18\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of -x^{2}+4x^{3}-27x-18 by each term of x-2.

$$-x^{3}+2x^{2}+4x^{4}-8x^{3}-27x^{2}+54x-18x+36$$

Combine -x^{3} and -8x^{3} to get -9x^{3}.

$$-9x^{3}+2x^{2}+4x^{4}-27x^{2}+54x-18x+36$$

Combine 2x^{2} and -27x^{2} to get -25x^{2}.

$$-9x^{3}-25x^{2}+4x^{4}+54x-18x+36$$

Combine 54x and -18x to get 36x.

$$-9x^{3}-25x^{2}+4x^{4}+36x+36$$

Expand

$$4x^{4}-9x^{3}-25x^{2}+36x+36$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of 4x+3.

$$\left(4x^{2}+3x-12x-9\right)\left(2+x\right)\left(x-2\right)$$

Combine 3x and -12x to get -9x.

$$\left(4x^{2}-9x-9\right)\left(2+x\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 4x^{2}-9x-9 by each term of 2+x.

$$\left(8x^{2}+4x^{3}-18x-9x^{2}-18-9x\right)\left(x-2\right)$$

Combine 8x^{2} and -9x^{2} to get -x^{2}.

$$\left(-x^{2}+4x^{3}-18x-18-9x\right)\left(x-2\right)$$

Combine -18x and -9x to get -27x.

$$\left(-x^{2}+4x^{3}-27x-18\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of -x^{2}+4x^{3}-27x-18 by each term of x-2.

$$-x^{3}+2x^{2}+4x^{4}-8x^{3}-27x^{2}+54x-18x+36$$

Combine -x^{3} and -8x^{3} to get -9x^{3}.

$$-9x^{3}+2x^{2}+4x^{4}-27x^{2}+54x-18x+36$$

Combine 2x^{2} and -27x^{2} to get -25x^{2}.

$$-9x^{3}-25x^{2}+4x^{4}+54x-18x+36$$

Combine 54x and -18x to get 36x.

$$-9x^{3}-25x^{2}+4x^{4}+36x+36$$