Solve x(4-x)-(x-3)(x+3)+x(x-6)

$$x ( 4 - x ) - ( x - 3 ) ( x + 3 ) + x ( x - 6 )$$

Evaluate

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

Solution Steps

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

$$4x-x^{2}-\left(x-3\right)\left(x+3\right)+x\left(x-6\right)$$

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}.

$$4x-x^{2}-\left(x^{2}-3^{2}\right)+x\left(x-6\right)$$

Calculate 3 to the power of 2 and get 9.

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

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

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

The opposite of -9 is 9.

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

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

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

Use the distributive property to multiply x by x-6.

$$4x-2x^{2}+9+x^{2}-6x$$

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

$$4x-x^{2}+9-6x$$

Combine 4x and -6x to get -2x.

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

Expand

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

Solution Steps

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

$$4x-x^{2}-\left(x-3\right)\left(x+3\right)+x\left(x-6\right)$$

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}.

$$4x-x^{2}-\left(x^{2}-3^{2}\right)+x\left(x-6\right)$$

Calculate 3 to the power of 2 and get 9.

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

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

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

The opposite of -9 is 9.

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

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

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

Use the distributive property to multiply x by x-6.

$$4x-2x^{2}+9+x^{2}-6x$$

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

$$4x-x^{2}+9-6x$$

Combine 4x and -6x to get -2x.

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