Solve (3+sqrt{3})(3-sqrt{3})m

$$( 3 + \sqrt { 3 } ) ( 3 - \sqrt { 3 } ) m$$

Evaluate

$$6m$$

Solution Steps

Apply the distributive property by multiplying each term of 3+\sqrt{3} by each term of 3-\sqrt{3}.

$$\left(9-3\sqrt{3}+3\sqrt{3}-\left(\sqrt{3}\right)^{2}\right)m$$

Combine -3\sqrt{3} and 3\sqrt{3} to get 0.

$$\left(9-\left(\sqrt{3}\right)^{2}\right)m$$

The square of \sqrt{3} is 3.

$$\left(9-3\right)m$$

Subtract 3 from 9 to get 6.

$$6m$$

Differentiate w.r.t. m

$$6$$

Steps Using Definition of a Derivative

Apply the distributive property by multiplying each term of 3+\sqrt{3} by each term of 3-\sqrt{3}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(9-3\sqrt{3}+3\sqrt{3}-\left(\sqrt{3}\right)^{2}\right)m)$$

Combine -3\sqrt{3} and 3\sqrt{3} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(9-\left(\sqrt{3}\right)^{2}\right)m)$$

The square of \sqrt{3} is 3.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\left(9-3\right)m)$$

Subtract 3 from 9 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}m}(6m)$$

The derivative of ax^{n} is nax^{n-1}.

$$6m^{1-1}$$

Subtract 1 from 1.

$$6m^{0}$$

For any term t except 0, t^{0}=1.

$$6\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6$$