Solve 3*x-3*1-2x*x+2x*1

$$3 \times x-3 \times 1-2x \times x+2x \times 1$$

Evaluate

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

Solution Steps

Multiply x and x to get x^{2}.

$$3x-3\times 1-2x^{2}+2x\times 1$$

Multiply 3 and 1 to get 3.

$$3x-3-2x^{2}+2x\times 1$$

Multiply 2 and 1 to get 2.

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

Combine 3x and 2x to get 5x.

$$5x-3-2x^{2}$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$-2x^{2}+5x-3$$

Factor the expression by grouping. First, the expression needs to be rewritten as -2x^{2}+ax+bx-3. To find a and b, set up a system to be solved.

$$a+b=5 ab=-2\left(-3\right)=6$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 6.

$$1,6 2,3$$

Calculate the sum for each pair.

$$1+6=7 2+3=5$$

The solution is the pair that gives sum 5.

$$a=3 b=2$$

Rewrite -2x^{2}+5x-3 as \left(-2x^{2}+3x\right)+\left(2x-3\right).

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

Factor out -x in -2x^{2}+3x.

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

Factor out common term 2x-3 by using distributive property.

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