Solve (x-7)(x-6)(x-5)(x-4)-1680

$$( x - 7 ) ( x - 6 ) ( x - 5 ) ( x - 4 ) - 1680$$

Evaluate

$$\left(x-12\right)\left(x+1\right)\left(x^{2}-11x+70\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-7 by each term of x-6.

$$\left(x^{2}-6x-7x+42\right)\left(x-5\right)\left(x-4\right)-1680$$

Combine -6x and -7x to get -13x.

$$\left(x^{2}-13x+42\right)\left(x-5\right)\left(x-4\right)-1680$$

Apply the distributive property by multiplying each term of x^{2}-13x+42 by each term of x-5.

$$\left(x^{3}-5x^{2}-13x^{2}+65x+42x-210\right)\left(x-4\right)-1680$$

Combine -5x^{2} and -13x^{2} to get -18x^{2}.

$$\left(x^{3}-18x^{2}+65x+42x-210\right)\left(x-4\right)-1680$$

Combine 65x and 42x to get 107x.

$$\left(x^{3}-18x^{2}+107x-210\right)\left(x-4\right)-1680$$

Apply the distributive property by multiplying each term of x^{3}-18x^{2}+107x-210 by each term of x-4.

$$x^{4}-4x^{3}-18x^{3}+72x^{2}+107x^{2}-428x-210x+840-1680$$

Combine -4x^{3} and -18x^{3} to get -22x^{3}.

$$x^{4}-22x^{3}+72x^{2}+107x^{2}-428x-210x+840-1680$$

Combine 72x^{2} and 107x^{2} to get 179x^{2}.

$$x^{4}-22x^{3}+179x^{2}-428x-210x+840-1680$$

Combine -428x and -210x to get -638x.

$$x^{4}-22x^{3}+179x^{2}-638x+840-1680$$

Subtract 1680 from 840 to get -840.

$$x^{4}-22x^{3}+179x^{2}-638x-840$$

Expand

$$x^{4}-22x^{3}+179x^{2}-638x-840$$

Solution Steps

Apply the distributive property by multiplying each term of x-7 by each term of x-6.

$$\left(x^{2}-6x-7x+42\right)\left(x-5\right)\left(x-4\right)-1680$$

Combine -6x and -7x to get -13x.

$$\left(x^{2}-13x+42\right)\left(x-5\right)\left(x-4\right)-1680$$

Apply the distributive property by multiplying each term of x^{2}-13x+42 by each term of x-5.

$$\left(x^{3}-5x^{2}-13x^{2}+65x+42x-210\right)\left(x-4\right)-1680$$

Combine -5x^{2} and -13x^{2} to get -18x^{2}.

$$\left(x^{3}-18x^{2}+65x+42x-210\right)\left(x-4\right)-1680$$

Combine 65x and 42x to get 107x.

$$\left(x^{3}-18x^{2}+107x-210\right)\left(x-4\right)-1680$$

Apply the distributive property by multiplying each term of x^{3}-18x^{2}+107x-210 by each term of x-4.

$$x^{4}-4x^{3}-18x^{3}+72x^{2}+107x^{2}-428x-210x+840-1680$$

Combine -4x^{3} and -18x^{3} to get -22x^{3}.

$$x^{4}-22x^{3}+72x^{2}+107x^{2}-428x-210x+840-1680$$

Combine 72x^{2} and 107x^{2} to get 179x^{2}.

$$x^{4}-22x^{3}+179x^{2}-428x-210x+840-1680$$

Combine -428x and -210x to get -638x.

$$x^{4}-22x^{3}+179x^{2}-638x+840-1680$$

Subtract 1680 from 840 to get -840.

$$x^{4}-22x^{3}+179x^{2}-638x-840$$