Solve 2left(2x^2+3x-1right)^2+3left(2x^2+3x-1right)-1

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

Evaluate

$$8x^{4}+24x^{3}+16x^{2}-3x-2$$

Solution Steps

Square 2x^{2}+3x-1.

$$2\left(4x^{4}+12x^{3}+5x^{2}-6x+1\right)+3\left(2x^{2}+3x-1\right)-1$$

Use the distributive property to multiply 2 by 4x^{4}+12x^{3}+5x^{2}-6x+1.

$$8x^{4}+24x^{3}+10x^{2}-12x+2+3\left(2x^{2}+3x-1\right)-1$$

Use the distributive property to multiply 3 by 2x^{2}+3x-1.

$$8x^{4}+24x^{3}+10x^{2}-12x+2+6x^{2}+9x-3-1$$

Combine 10x^{2} and 6x^{2} to get 16x^{2}.

$$8x^{4}+24x^{3}+16x^{2}-12x+2+9x-3-1$$

Combine -12x and 9x to get -3x.

$$8x^{4}+24x^{3}+16x^{2}-3x+2-3-1$$

Subtract 3 from 2 to get -1.

$$8x^{4}+24x^{3}+16x^{2}-3x-1-1$$

Subtract 1 from -1 to get -2.

$$8x^{4}+24x^{3}+16x^{2}-3x-2$$

Expand

$$8x^{4}+24x^{3}+16x^{2}-3x-2$$

Solution Steps

Square 2x^{2}+3x-1.

$$2\left(4x^{4}+12x^{3}+5x^{2}-6x+1\right)+3\left(2x^{2}+3x-1\right)-1$$

Use the distributive property to multiply 2 by 4x^{4}+12x^{3}+5x^{2}-6x+1.

$$8x^{4}+24x^{3}+10x^{2}-12x+2+3\left(2x^{2}+3x-1\right)-1$$

Use the distributive property to multiply 3 by 2x^{2}+3x-1.

$$8x^{4}+24x^{3}+10x^{2}-12x+2+6x^{2}+9x-3-1$$

Combine 10x^{2} and 6x^{2} to get 16x^{2}.

$$8x^{4}+24x^{3}+16x^{2}-12x+2+9x-3-1$$

Combine -12x and 9x to get -3x.

$$8x^{4}+24x^{3}+16x^{2}-3x+2-3-1$$

Subtract 3 from 2 to get -1.

$$8x^{4}+24x^{3}+16x^{2}-3x-1-1$$

Subtract 1 from -1 to get -2.

$$8x^{4}+24x^{3}+16x^{2}-3x-2$$