Solve (5sqrt{c}+sqrt{d})(5sqrt{c}-sqrt{d})

$$( 5 \sqrt { c } + \sqrt { d } ) ( 5 \sqrt { c } - \sqrt { d } )$$

Evaluate

$$25c-d$$

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}.

$$\left(5\sqrt{c}\right)^{2}-\left(\sqrt{d}\right)^{2}$$

Expand \left(5\sqrt{c}\right)^{2}.

$$5^{2}\left(\sqrt{c}\right)^{2}-\left(\sqrt{d}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25\left(\sqrt{c}\right)^{2}-\left(\sqrt{d}\right)^{2}$$

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

$$25c-\left(\sqrt{d}\right)^{2}$$

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

$$25c-d$$

Differentiate w.r.t. c

$$25$$