Solve (3-x)^2-(2-x)(3+x)

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

Evaluate

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

Solution Steps

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

$$9-6x+x^{2}-\left(2-x\right)\left(3+x\right)$$

Use the distributive property to multiply 2-x by 3+x and combine like terms.

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

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

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

Subtract 6 from 9 to get 3.

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

Combine -6x and x to get -5x.

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

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

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

Expand

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

Solution Steps

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

$$9-6x+x^{2}-\left(2-x\right)\left(3+x\right)$$

Use the distributive property to multiply 2-x by 3+x and combine like terms.

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

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

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

Subtract 6 from 9 to get 3.

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

Combine -6x and x to get -5x.

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

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

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