Solve (x(x-3)(x-2)(x-1))((x-4)-3)

$$( x ( x - 3 ) ( x - 2 ) ( x - 1 ) ) ( ( x - 4 ) - 3 )$$

Evaluate

$$x\left(x-7\right)\left(x-3\right)\left(x-2\right)\left(x-1\right)$$

Solution Steps

Subtract 3 from -4 to get -7.

$$x\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x-7\right)$$

Use the distributive property to multiply x by x-3.

$$\left(x^{2}-3x\right)\left(x-2\right)\left(x-1\right)\left(x-7\right)$$

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

$$\left(x^{3}-2x^{2}-3x^{2}+6x\right)\left(x-1\right)\left(x-7\right)$$

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

$$\left(x^{3}-5x^{2}+6x\right)\left(x-1\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{3}-5x^{2}+6x by each term of x-1.

$$\left(x^{4}-x^{3}-5x^{3}+5x^{2}+6x^{2}-6x\right)\left(x-7\right)$$

Combine -x^{3} and -5x^{3} to get -6x^{3}.

$$\left(x^{4}-6x^{3}+5x^{2}+6x^{2}-6x\right)\left(x-7\right)$$

Combine 5x^{2} and 6x^{2} to get 11x^{2}.

$$\left(x^{4}-6x^{3}+11x^{2}-6x\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{4}-6x^{3}+11x^{2}-6x by each term of x-7.

$$x^{5}-7x^{4}-6x^{4}+42x^{3}+11x^{3}-77x^{2}-6x^{2}+42x$$

Combine -7x^{4} and -6x^{4} to get -13x^{4}.

$$x^{5}-13x^{4}+42x^{3}+11x^{3}-77x^{2}-6x^{2}+42x$$

Combine 42x^{3} and 11x^{3} to get 53x^{3}.

$$x^{5}-13x^{4}+53x^{3}-77x^{2}-6x^{2}+42x$$

Combine -77x^{2} and -6x^{2} to get -83x^{2}.

$$x^{5}-13x^{4}+53x^{3}-83x^{2}+42x$$

Expand

$$x^{5}-13x^{4}+53x^{3}-83x^{2}+42x$$

Solution Steps

Subtract 3 from -4 to get -7.

$$x\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x-7\right)$$

Use the distributive property to multiply x by x-3.

$$\left(x^{2}-3x\right)\left(x-2\right)\left(x-1\right)\left(x-7\right)$$

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

$$\left(x^{3}-2x^{2}-3x^{2}+6x\right)\left(x-1\right)\left(x-7\right)$$

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

$$\left(x^{3}-5x^{2}+6x\right)\left(x-1\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{3}-5x^{2}+6x by each term of x-1.

$$\left(x^{4}-x^{3}-5x^{3}+5x^{2}+6x^{2}-6x\right)\left(x-7\right)$$

Combine -x^{3} and -5x^{3} to get -6x^{3}.

$$\left(x^{4}-6x^{3}+5x^{2}+6x^{2}-6x\right)\left(x-7\right)$$

Combine 5x^{2} and 6x^{2} to get 11x^{2}.

$$\left(x^{4}-6x^{3}+11x^{2}-6x\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{4}-6x^{3}+11x^{2}-6x by each term of x-7.

$$x^{5}-7x^{4}-6x^{4}+42x^{3}+11x^{3}-77x^{2}-6x^{2}+42x$$

Combine -7x^{4} and -6x^{4} to get -13x^{4}.

$$x^{5}-13x^{4}+42x^{3}+11x^{3}-77x^{2}-6x^{2}+42x$$

Combine 42x^{3} and 11x^{3} to get 53x^{3}.

$$x^{5}-13x^{4}+53x^{3}-77x^{2}-6x^{2}+42x$$

Combine -77x^{2} and -6x^{2} to get -83x^{2}.

$$x^{5}-13x^{4}+53x^{3}-83x^{2}+42x$$