Solve left(-15-xright)left(-7-xright)left(21-xright)+15*8*16+18*6*19+19*16(-7-x)+18*8(-15-x)-6*15(21-x)

$$\left( -15-x \right) \left( -7-x \right) \left( 21-x \right) +15 \times 8 \times 16+18 \times 6 \times 19+19 \times 16(-7-x)+18 \times 8(-15-x)-6 \times 15(21-x)$$

Evaluate

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

Solution Steps

Multiply 15 and 8 to get 120. Multiply 18 and 6 to get 108. Multiply 19 and 16 to get 304. Multiply 18 and 8 to get 144.

$$\left(-15-x\right)\left(-7-x\right)\left(21-x\right)+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Apply the distributive property by multiplying each term of -15-x by each term of -7-x.

$$\left(105+15x+7x+x^{2}\right)\left(21-x\right)+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine 15x and 7x to get 22x.

$$\left(105+22x+x^{2}\right)\left(21-x\right)+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Apply the distributive property by multiplying each term of 105+22x+x^{2} by each term of 21-x.

$$2205-105x+462x-22x^{2}+21x^{2}-x^{3}+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine -105x and 462x to get 357x.

$$2205+357x-22x^{2}+21x^{2}-x^{3}+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine -22x^{2} and 21x^{2} to get -x^{2}.

$$2205+357x-x^{2}-x^{3}+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Multiply 120 and 16 to get 1920.

$$2205+357x-x^{2}-x^{3}+1920+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Add 2205 and 1920 to get 4125.

$$4125+357x-x^{2}-x^{3}+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Multiply 108 and 19 to get 2052.

$$4125+357x-x^{2}-x^{3}+2052+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Add 4125 and 2052 to get 6177.

$$6177+357x-x^{2}-x^{3}+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Use the distributive property to multiply 304 by -7-x.

$$6177+357x-x^{2}-x^{3}-2128-304x+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Subtract 2128 from 6177 to get 4049.

$$4049+357x-x^{2}-x^{3}-304x+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine 357x and -304x to get 53x.

$$4049+53x-x^{2}-x^{3}+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Use the distributive property to multiply 144 by -15-x.

$$4049+53x-x^{2}-x^{3}-2160-144x-6\times 15\left(21-x\right)$$

Subtract 2160 from 4049 to get 1889.

$$1889+53x-x^{2}-x^{3}-144x-6\times 15\left(21-x\right)$$

Combine 53x and -144x to get -91x.

$$1889-91x-x^{2}-x^{3}-6\times 15\left(21-x\right)$$

Multiply 6 and 15 to get 90.

$$1889-91x-x^{2}-x^{3}-90\left(21-x\right)$$

Use the distributive property to multiply -90 by 21-x.

$$1889-91x-x^{2}-x^{3}-1890+90x$$

Subtract 1890 from 1889 to get -1.

$$-1-91x-x^{2}-x^{3}+90x$$

Combine -91x and 90x to get -x.

$$-1-x-x^{2}-x^{3}$$

Expand

$$-x^{3}-x^{2}-x-1$$

Solution Steps

Multiply 15 and 8 to get 120. Multiply 18 and 6 to get 108. Multiply 19 and 16 to get 304. Multiply 18 and 8 to get 144.

$$\left(-15-x\right)\left(-7-x\right)\left(21-x\right)+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Apply the distributive property by multiplying each term of -15-x by each term of -7-x.

$$\left(105+15x+7x+x^{2}\right)\left(21-x\right)+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine 15x and 7x to get 22x.

$$\left(105+22x+x^{2}\right)\left(21-x\right)+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Apply the distributive property by multiplying each term of 105+22x+x^{2} by each term of 21-x.

$$2205-105x+462x-22x^{2}+21x^{2}-x^{3}+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine -105x and 462x to get 357x.

$$2205+357x-22x^{2}+21x^{2}-x^{3}+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine -22x^{2} and 21x^{2} to get -x^{2}.

$$2205+357x-x^{2}-x^{3}+120\times 16+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Multiply 120 and 16 to get 1920.

$$2205+357x-x^{2}-x^{3}+1920+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Add 2205 and 1920 to get 4125.

$$4125+357x-x^{2}-x^{3}+108\times 19+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Multiply 108 and 19 to get 2052.

$$4125+357x-x^{2}-x^{3}+2052+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Add 4125 and 2052 to get 6177.

$$6177+357x-x^{2}-x^{3}+304\left(-7-x\right)+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Use the distributive property to multiply 304 by -7-x.

$$6177+357x-x^{2}-x^{3}-2128-304x+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Subtract 2128 from 6177 to get 4049.

$$4049+357x-x^{2}-x^{3}-304x+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Combine 357x and -304x to get 53x.

$$4049+53x-x^{2}-x^{3}+144\left(-15-x\right)-6\times 15\left(21-x\right)$$

Use the distributive property to multiply 144 by -15-x.

$$4049+53x-x^{2}-x^{3}-2160-144x-6\times 15\left(21-x\right)$$

Subtract 2160 from 4049 to get 1889.

$$1889+53x-x^{2}-x^{3}-144x-6\times 15\left(21-x\right)$$

Combine 53x and -144x to get -91x.

$$1889-91x-x^{2}-x^{3}-6\times 15\left(21-x\right)$$

Multiply 6 and 15 to get 90.

$$1889-91x-x^{2}-x^{3}-90\left(21-x\right)$$

Use the distributive property to multiply -90 by 21-x.

$$1889-91x-x^{2}-x^{3}-1890+90x$$

Subtract 1890 from 1889 to get -1.

$$-1-91x-x^{2}-x^{3}+90x$$

Combine -91x and 90x to get -x.

$$-1-x-x^{2}-x^{3}$$