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

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

Evaluate

$$5\left(x+2\right)$$

Solution Steps

Use the distributive property to multiply 3x by x+2.

$$3x^{2}+6x-\left(x-1\right)-\left(x+3\right)\left(x-3\right)-2x^{2}$$

To find the opposite of x-1, find the opposite of each term.

$$3x^{2}+6x-x+1-\left(x+3\right)\left(x-3\right)-2x^{2}$$

Combine 6x and -x to get 5x.

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

Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$3x^{2}+5x+1-\left(x^{2}-9\right)-2x^{2}$$

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

$$3x^{2}+5x+1-x^{2}+9-2x^{2}$$

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

$$2x^{2}+5x+1+9-2x^{2}$$

Add 1 and 9 to get 10.

$$2x^{2}+5x+10-2x^{2}$$

Combine 2x^{2} and -2x^{2} to get 0.

$$5x+10$$

Expand

$$5x+10$$

Solution Steps

Use the distributive property to multiply 3x by x+2.

$$3x^{2}+6x-\left(x-1\right)-\left(x+3\right)\left(x-3\right)-2x^{2}$$

To find the opposite of x-1, find the opposite of each term.

$$3x^{2}+6x-x+1-\left(x+3\right)\left(x-3\right)-2x^{2}$$

Combine 6x and -x to get 5x.

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

Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$3x^{2}+5x+1-\left(x^{2}-9\right)-2x^{2}$$

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

$$3x^{2}+5x+1-x^{2}+9-2x^{2}$$

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

$$2x^{2}+5x+1+9-2x^{2}$$

Add 1 and 9 to get 10.

$$2x^{2}+5x+10-2x^{2}$$

Combine 2x^{2} and -2x^{2} to get 0.

$$5x+10$$