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

$$(3x+2)(2x+3)-(x-1)(x-1)$$

Evaluate

$$5\left(x^{2}+3x+1\right)$$

Solution Steps

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

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

Apply the distributive property by multiplying each term of 3x+2 by each term of 2x+3.

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

Combine 9x and 4x to get 13x.

$$6x^{2}+13x+6-\left(x-1\right)^{2}$$

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

$$6x^{2}+13x+6-\left(x^{2}-2x+1\right)$$

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$6x^{2}+13x+6-x^{2}-\left(-2x\right)-1$$

The opposite of -2x is 2x.

$$6x^{2}+13x+6-x^{2}+2x-1$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}+13x+6+2x-1$$

Combine 13x and 2x to get 15x.

$$5x^{2}+15x+6-1$$

Subtract 1 from 6 to get 5.

$$5x^{2}+15x+5$$

Expand

$$5x^{2}+15x+5$$

Solution Steps

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

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

Apply the distributive property by multiplying each term of 3x+2 by each term of 2x+3.

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

Combine 9x and 4x to get 13x.

$$6x^{2}+13x+6-\left(x-1\right)^{2}$$

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

$$6x^{2}+13x+6-\left(x^{2}-2x+1\right)$$

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$6x^{2}+13x+6-x^{2}-\left(-2x\right)-1$$

The opposite of -2x is 2x.

$$6x^{2}+13x+6-x^{2}+2x-1$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}+13x+6+2x-1$$

Combine 13x and 2x to get 15x.

$$5x^{2}+15x+6-1$$

Subtract 1 from 6 to get 5.

$$5x^{2}+15x+5$$