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

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

Evaluate

$$19x^{2}-15x+1$$

Solution Steps

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

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

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

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

Multiply -1 and 1 to get -1.

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

Use the distributive property to multiply -x by 3x-3.

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

Combine 4x and 3x to get 7x.

$$16x^{2}-8x+1-\left(7x-3x^{2}\right)$$

To find the opposite of 7x-3x^{2}, find the opposite of each term.

$$16x^{2}-8x+1-7x-\left(-3x^{2}\right)$$

The opposite of -3x^{2} is 3x^{2}.

$$16x^{2}-8x+1-7x+3x^{2}$$

Combine -8x and -7x to get -15x.

$$16x^{2}-15x+1+3x^{2}$$

Combine 16x^{2} and 3x^{2} to get 19x^{2}.

$$19x^{2}-15x+1$$

Expand

$$19x^{2}-15x+1$$

Solution Steps

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

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

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

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

Multiply -1 and 1 to get -1.

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

Use the distributive property to multiply -x by 3x-3.

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

Combine 4x and 3x to get 7x.

$$16x^{2}-8x+1-\left(7x-3x^{2}\right)$$

To find the opposite of 7x-3x^{2}, find the opposite of each term.

$$16x^{2}-8x+1-7x-\left(-3x^{2}\right)$$

The opposite of -3x^{2} is 3x^{2}.

$$16x^{2}-8x+1-7x+3x^{2}$$

Combine -8x and -7x to get -15x.

$$16x^{2}-15x+1+3x^{2}$$

Combine 16x^{2} and 3x^{2} to get 19x^{2}.

$$19x^{2}-15x+1$$