Solve (2x^2-3x-2)(x^2-5)+(x^2-5)(2x^2-3x-2)

$$( 2 x ^ { 2 } - 3 x - 2 ) ( x ^ { 2 } - 5 ) + ( x ^ { 2 } - 5 ) ( 2 x ^ { 2 } - 3 x - 2 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 2x^{2}-3x-2 by x^{2}-5 and combine like terms.

$$2x^{4}-12x^{2}-3x^{3}+15x+10+\left(x^{2}-5\right)\left(2x^{2}-3x-2\right)$$

Use the distributive property to multiply x^{2}-5 by 2x^{2}-3x-2 and combine like terms.

$$2x^{4}-12x^{2}-3x^{3}+15x+10+2x^{4}-3x^{3}-12x^{2}+15x+10$$

Combine 2x^{4} and 2x^{4} to get 4x^{4}.

$$4x^{4}-12x^{2}-3x^{3}+15x+10-3x^{3}-12x^{2}+15x+10$$

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

$$4x^{4}-12x^{2}-6x^{3}+15x+10-12x^{2}+15x+10$$

Combine -12x^{2} and -12x^{2} to get -24x^{2}.

$$4x^{4}-24x^{2}-6x^{3}+15x+10+15x+10$$

Combine 15x and 15x to get 30x.

$$4x^{4}-24x^{2}-6x^{3}+30x+10+10$$

Add 10 and 10 to get 20.

$$4x^{4}-24x^{2}-6x^{3}+30x+20$$

Expand

$$4x^{4}-6x^{3}-24x^{2}+30x+20$$

Solution Steps

Use the distributive property to multiply 2x^{2}-3x-2 by x^{2}-5 and combine like terms.

$$2x^{4}-12x^{2}-3x^{3}+15x+10+\left(x^{2}-5\right)\left(2x^{2}-3x-2\right)$$

Use the distributive property to multiply x^{2}-5 by 2x^{2}-3x-2 and combine like terms.

$$2x^{4}-12x^{2}-3x^{3}+15x+10+2x^{4}-3x^{3}-12x^{2}+15x+10$$

Combine 2x^{4} and 2x^{4} to get 4x^{4}.

$$4x^{4}-12x^{2}-3x^{3}+15x+10-3x^{3}-12x^{2}+15x+10$$

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

$$4x^{4}-12x^{2}-6x^{3}+15x+10-12x^{2}+15x+10$$

Combine -12x^{2} and -12x^{2} to get -24x^{2}.

$$4x^{4}-24x^{2}-6x^{3}+15x+10+15x+10$$

Combine 15x and 15x to get 30x.

$$4x^{4}-24x^{2}-6x^{3}+30x+10+10$$

Add 10 and 10 to get 20.

$$4x^{4}-24x^{2}-6x^{3}+30x+20$$