Solve (1)(2sqrt{2}+3)(2sqrt{2}-3)

$$( 1 ) ( 2 \sqrt { 2 } + 3 ) ( 2 \sqrt { 2 } - 3 )$$

Evaluate

$$-1$$

Solution Steps

Use the distributive property to multiply 1 by 2\sqrt{2}+3.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{2} is 2.

$$4\times 2-3^{2}$$

Multiply 4 and 2 to get 8.

$$8-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$8-9$$

Subtract 9 from 8 to get -1.

$$-1$$

Factor

$$-1$$