Solve (1)(4+sqrt{7})(4-sqrt{7})

$$( 1 ) ( 4 + \sqrt { 7 } ) ( 4 - \sqrt { 7 } )$$

Evaluate

$$9$$

Solution Steps

Use the distributive property to multiply 1 by 4+\sqrt{7}.

$$\left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)$$

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

$$4^{2}-\left(\sqrt{7}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16-\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$16-7$$

Subtract 7 from 16 to get 9.

$$9$$

Factor

$$3^{2}$$