Solve (2x-27)*(x^2+18x+81)-(x^2-27x-19)*(2x+18)

$$( 2 x - 27 ) \times ( x ^ { 2 } + 18 x + 81 ) - ( x ^ { 2 } - 27 x - 19 ) \times ( 2 x + 18 )$$

Evaluate

$$5\left(9x-41\right)\left(x+9\right)$$

Solution Steps

Use the distributive property to multiply 2x-27 by x^{2}+18x+81 and combine like terms.

$$2x^{3}+9x^{2}-324x-2187-\left(x^{2}-27x-19\right)\left(2x+18\right)$$

Use the distributive property to multiply x^{2}-27x-19 by 2x+18 and combine like terms.

$$2x^{3}+9x^{2}-324x-2187-\left(2x^{3}-36x^{2}-524x-342\right)$$

To find the opposite of 2x^{3}-36x^{2}-524x-342, find the opposite of each term.

$$2x^{3}+9x^{2}-324x-2187-2x^{3}+36x^{2}+524x+342$$

Combine 2x^{3} and -2x^{3} to get 0.

$$9x^{2}-324x-2187+36x^{2}+524x+342$$

Combine 9x^{2} and 36x^{2} to get 45x^{2}.

$$45x^{2}-324x-2187+524x+342$$

Combine -324x and 524x to get 200x.

$$45x^{2}+200x-2187+342$$

Add -2187 and 342 to get -1845.

$$45x^{2}+200x-1845$$

Expand

$$45x^{2}+200x-1845$$

Solution Steps

Use the distributive property to multiply 2x-27 by x^{2}+18x+81 and combine like terms.

$$2x^{3}+9x^{2}-324x-2187-\left(x^{2}-27x-19\right)\left(2x+18\right)$$

Use the distributive property to multiply x^{2}-27x-19 by 2x+18 and combine like terms.

$$2x^{3}+9x^{2}-324x-2187-\left(2x^{3}-36x^{2}-524x-342\right)$$

To find the opposite of 2x^{3}-36x^{2}-524x-342, find the opposite of each term.

$$2x^{3}+9x^{2}-324x-2187-2x^{3}+36x^{2}+524x+342$$

Combine 2x^{3} and -2x^{3} to get 0.

$$9x^{2}-324x-2187+36x^{2}+524x+342$$

Combine 9x^{2} and 36x^{2} to get 45x^{2}.

$$45x^{2}-324x-2187+524x+342$$

Combine -324x and 524x to get 200x.

$$45x^{2}+200x-2187+342$$

Add -2187 and 342 to get -1845.

$$45x^{2}+200x-1845$$