Solve =3x(x-4)-(x+3)(x-1)+(x-3)^2

$$= 3 x ( x - 4 ) - ( x + 3 ) ( x - 1 ) + ( x - 3 ) ^ { 2 }$$

Evaluate

$$\left(x-6\right)\left(3x-2\right)$$

Solution Steps

Use the distributive property to multiply 3x by x-4.

$$3x^{2}-12x-\left(x+3\right)\left(x-1\right)+\left(x-3\right)^{2}$$

Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$3x^{2}-12x-\left(x^{2}+2x-3\right)+\left(x-3\right)^{2}$$

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

$$3x^{2}-12x-x^{2}-2x+3+\left(x-3\right)^{2}$$

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

$$2x^{2}-12x-2x+3+\left(x-3\right)^{2}$$

Combine -12x and -2x to get -14x.

$$2x^{2}-14x+3+\left(x-3\right)^{2}$$

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

$$2x^{2}-14x+3+x^{2}-6x+9$$

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

$$3x^{2}-14x+3-6x+9$$

Combine -14x and -6x to get -20x.

$$3x^{2}-20x+3+9$$

Add 3 and 9 to get 12.

$$3x^{2}-20x+12$$

Expand

$$3x^{2}-20x+12$$

Solution Steps

Use the distributive property to multiply 3x by x-4.

$$3x^{2}-12x-\left(x+3\right)\left(x-1\right)+\left(x-3\right)^{2}$$

Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$3x^{2}-12x-\left(x^{2}+2x-3\right)+\left(x-3\right)^{2}$$

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

$$3x^{2}-12x-x^{2}-2x+3+\left(x-3\right)^{2}$$

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

$$2x^{2}-12x-2x+3+\left(x-3\right)^{2}$$

Combine -12x and -2x to get -14x.

$$2x^{2}-14x+3+\left(x-3\right)^{2}$$

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

$$2x^{2}-14x+3+x^{2}-6x+9$$

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

$$3x^{2}-14x+3-6x+9$$

Combine -14x and -6x to get -20x.

$$3x^{2}-20x+3+9$$

Add 3 and 9 to get 12.

$$3x^{2}-20x+12$$