Solve (-1)(3x-1)+(2x-5)^2-(8x+1)(2x-1)

$$( - 1 ) ( 3 x - 1 ) + ( 2 x - 5 ) ^ { 2 } - ( 8 x + 1 ) ( 2 x - 1 )$$

Evaluate

$$27-17x-12x^{2}$$

Solution Steps

To find the opposite of 3x-1, find the opposite of each term.

$$-3x+1+\left(2x-5\right)^{2}-\left(8x+1\right)\left(2x-1\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$-3x+1+4x^{2}-20x+25-\left(8x+1\right)\left(2x-1\right)$$

Combine -3x and -20x to get -23x.

$$-23x+1+4x^{2}+25-\left(8x+1\right)\left(2x-1\right)$$

Add 1 and 25 to get 26.

$$-23x+26+4x^{2}-\left(8x+1\right)\left(2x-1\right)$$

Use the distributive property to multiply 8x+1 by 2x-1 and combine like terms.

$$-23x+26+4x^{2}-\left(16x^{2}-6x-1\right)$$

To find the opposite of 16x^{2}-6x-1, find the opposite of each term.

$$-23x+26+4x^{2}-16x^{2}+6x+1$$

Combine 4x^{2} and -16x^{2} to get -12x^{2}.

$$-23x+26-12x^{2}+6x+1$$

Combine -23x and 6x to get -17x.

$$-17x+26-12x^{2}+1$$

Add 26 and 1 to get 27.

$$-17x+27-12x^{2}$$

Expand

$$27-17x-12x^{2}$$

Solution Steps

To find the opposite of 3x-1, find the opposite of each term.

$$-3x+1+\left(2x-5\right)^{2}-\left(8x+1\right)\left(2x-1\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$-3x+1+4x^{2}-20x+25-\left(8x+1\right)\left(2x-1\right)$$

Combine -3x and -20x to get -23x.

$$-23x+1+4x^{2}+25-\left(8x+1\right)\left(2x-1\right)$$

Add 1 and 25 to get 26.

$$-23x+26+4x^{2}-\left(8x+1\right)\left(2x-1\right)$$

Use the distributive property to multiply 8x+1 by 2x-1 and combine like terms.

$$-23x+26+4x^{2}-\left(16x^{2}-6x-1\right)$$

To find the opposite of 16x^{2}-6x-1, find the opposite of each term.

$$-23x+26+4x^{2}-16x^{2}+6x+1$$

Combine 4x^{2} and -16x^{2} to get -12x^{2}.

$$-23x+26-12x^{2}+6x+1$$

Combine -23x and 6x to get -17x.

$$-17x+26-12x^{2}+1$$

Add 26 and 1 to get 27.

$$-17x+27-12x^{2}$$