Solve (3sqrt{c}+sqrt{d})(3sqrt{c}-sqrt{d})

$$( 3 \sqrt { c } + \sqrt { d } ) ( 3 \sqrt { c } - \sqrt { d } )$$

Evaluate

$$9c-d$$

Solution Steps

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

$$\left(3\sqrt{c}\right)^{2}-\left(\sqrt{d}\right)^{2}$$

Expand \left(3\sqrt{c}\right)^{2}.

$$3^{2}\left(\sqrt{c}\right)^{2}-\left(\sqrt{d}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{c}\right)^{2}-\left(\sqrt{d}\right)^{2}$$

Calculate \sqrt{c} to the power of 2 and get c.

$$9c-\left(\sqrt{d}\right)^{2}$$

Calculate \sqrt{d} to the power of 2 and get d.

$$9c-d$$

Differentiate w.r.t. c

$$9$$