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

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

Evaluate

$$3x-16$$

Solution Steps

Consider \left(x+4\right)\left(x-4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}-16-x\left(x-3\right)$$

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

$$x^{2}-16-\left(x^{2}-3x\right)$$

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

$$x^{2}-16-x^{2}-\left(-3x\right)$$

The opposite of -3x is 3x.

$$x^{2}-16-x^{2}+3x$$

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

$$-16+3x$$

Expand

$$3x-16$$

Solution Steps

Consider \left(x+4\right)\left(x-4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}-16-x\left(x-3\right)$$

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

$$x^{2}-16-\left(x^{2}-3x\right)$$

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

$$x^{2}-16-x^{2}-\left(-3x\right)$$

The opposite of -3x is 3x.

$$x^{2}-16-x^{2}+3x$$

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

$$-16+3x$$