Solve 1-(3sqrt{7}+8)(3sqrt{7}-8)

$$1 - ( 3 \sqrt { 7 } + 8 ) ( 3 \sqrt { 7 } - 8 )$$

Evaluate

$$2$$

Solution Steps

Consider \left(3\sqrt{7}+8\right)\left(3\sqrt{7}-8\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$1-\left(\left(3\sqrt{7}\right)^{2}-8^{2}\right)$$

Expand \left(3\sqrt{7}\right)^{2}.

$$1-\left(3^{2}\left(\sqrt{7}\right)^{2}-8^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$1-\left(9\left(\sqrt{7}\right)^{2}-8^{2}\right)$$

The square of \sqrt{7} is 7.

$$1-\left(9\times 7-8^{2}\right)$$

Multiply 9 and 7 to get 63.

$$1-\left(63-8^{2}\right)$$

Calculate 8 to the power of 2 and get 64.

$$1-\left(63-64\right)$$

Subtract 64 from 63 to get -1.

$$1-\left(-1\right)$$

The opposite of -1 is 1.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Factor

$$2$$