Solve (4x-1)*(4x-1)-(4x-4)*(2x-3)

$$( 4 x - 1 ) \times ( 4 x - 1 ) - ( 4 x - 4 ) \times ( 2 x - 3 )$$

Evaluate

$$8x^{2}+12x-11$$

Solution Steps

Multiply 4x-1 and 4x-1 to get \left(4x-1\right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.

$$16x^{2}-8x+1-\left(4x-4\right)\left(2x-3\right)$$

Apply the distributive property by multiplying each term of 4x-4 by each term of 2x-3.

$$16x^{2}-8x+1-\left(8x^{2}-12x-8x+12\right)$$

Combine -12x and -8x to get -20x.

$$16x^{2}-8x+1-\left(8x^{2}-20x+12\right)$$

To find the opposite of 8x^{2}-20x+12, find the opposite of each term.

$$16x^{2}-8x+1-8x^{2}-\left(-20x\right)-12$$

The opposite of -20x is 20x.

$$16x^{2}-8x+1-8x^{2}+20x-12$$

Combine 16x^{2} and -8x^{2} to get 8x^{2}.

$$8x^{2}-8x+1+20x-12$$

Combine -8x and 20x to get 12x.

$$8x^{2}+12x+1-12$$

Subtract 12 from 1 to get -11.

$$8x^{2}+12x-11$$

Expand

$$8x^{2}+12x-11$$

Solution Steps

Multiply 4x-1 and 4x-1 to get \left(4x-1\right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.

$$16x^{2}-8x+1-\left(4x-4\right)\left(2x-3\right)$$

Apply the distributive property by multiplying each term of 4x-4 by each term of 2x-3.

$$16x^{2}-8x+1-\left(8x^{2}-12x-8x+12\right)$$

Combine -12x and -8x to get -20x.

$$16x^{2}-8x+1-\left(8x^{2}-20x+12\right)$$

To find the opposite of 8x^{2}-20x+12, find the opposite of each term.

$$16x^{2}-8x+1-8x^{2}-\left(-20x\right)-12$$

The opposite of -20x is 20x.

$$16x^{2}-8x+1-8x^{2}+20x-12$$

Combine 16x^{2} and -8x^{2} to get 8x^{2}.

$$8x^{2}-8x+1+20x-12$$

Combine -8x and 20x to get 12x.

$$8x^{2}+12x+1-12$$

Subtract 12 from 1 to get -11.

$$8x^{2}+12x-11$$