Solve (3x-4)^2-(6x-8)(2x+1)+9x^2-16

$$( 3 x - 4 ) ^ { 2 } - ( 6 x - 8 ) ( 2 x + 1 ) + 9 x ^ { 2 } - 16$$

Evaluate

$$2\left(x-1\right)\left(3x-4\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4\right)^{2}.

$$9x^{2}-24x+16-\left(6x-8\right)\left(2x+1\right)+9x^{2}-16$$

Use the distributive property to multiply 6x-8 by 2x+1 and combine like terms.

$$9x^{2}-24x+16-\left(12x^{2}-10x-8\right)+9x^{2}-16$$

To find the opposite of 12x^{2}-10x-8, find the opposite of each term.

$$9x^{2}-24x+16-12x^{2}+10x+8+9x^{2}-16$$

Combine 9x^{2} and -12x^{2} to get -3x^{2}.

$$-3x^{2}-24x+16+10x+8+9x^{2}-16$$

Combine -24x and 10x to get -14x.

$$-3x^{2}-14x+16+8+9x^{2}-16$$

Add 16 and 8 to get 24.

$$-3x^{2}-14x+24+9x^{2}-16$$

Combine -3x^{2} and 9x^{2} to get 6x^{2}.

$$6x^{2}-14x+24-16$$

Subtract 16 from 24 to get 8.

$$6x^{2}-14x+8$$

Expand

$$6x^{2}-14x+8$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-4\right)^{2}.

$$9x^{2}-24x+16-\left(6x-8\right)\left(2x+1\right)+9x^{2}-16$$

Use the distributive property to multiply 6x-8 by 2x+1 and combine like terms.

$$9x^{2}-24x+16-\left(12x^{2}-10x-8\right)+9x^{2}-16$$

To find the opposite of 12x^{2}-10x-8, find the opposite of each term.

$$9x^{2}-24x+16-12x^{2}+10x+8+9x^{2}-16$$

Combine 9x^{2} and -12x^{2} to get -3x^{2}.

$$-3x^{2}-24x+16+10x+8+9x^{2}-16$$

Combine -24x and 10x to get -14x.

$$-3x^{2}-14x+16+8+9x^{2}-16$$

Add 16 and 8 to get 24.

$$-3x^{2}-14x+24+9x^{2}-16$$

Combine -3x^{2} and 9x^{2} to get 6x^{2}.

$$6x^{2}-14x+24-16$$

Subtract 16 from 24 to get 8.

$$6x^{2}-14x+8$$