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

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

Evaluate

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

Solution Steps

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

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

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

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

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

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

$$4x^{2}-4x+1-\left(x^{2}-6x+9\right)$$

To find the opposite of x^{2}-6x+9, find the opposite of each term.

$$4x^{2}-4x+1-x^{2}-\left(-6x\right)-9$$

The opposite of -6x is 6x.

$$4x^{2}-4x+1-x^{2}+6x-9$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-4x+1+6x-9$$

Combine -4x and 6x to get 2x.

$$3x^{2}+2x+1-9$$

Subtract 9 from 1 to get -8.

$$3x^{2}+2x-8$$

Expand

$$3x^{2}+2x-8$$

Solution Steps

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

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

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

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

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

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

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

$$4x^{2}-4x+1-\left(x^{2}-6x+9\right)$$

To find the opposite of x^{2}-6x+9, find the opposite of each term.

$$4x^{2}-4x+1-x^{2}-\left(-6x\right)-9$$

The opposite of -6x is 6x.

$$4x^{2}-4x+1-x^{2}+6x-9$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-4x+1+6x-9$$

Combine -4x and 6x to get 2x.

$$3x^{2}+2x+1-9$$

Subtract 9 from 1 to get -8.

$$3x^{2}+2x-8$$