Solve 3*(2+sqrt{7})^2-12*(2+sqrt{7})+13

$$3 \times ( 2 + \sqrt { 7 } ) ^ { 2 } - 12 \times ( 2 + \sqrt { 7 } ) + 13$$

Evaluate

$$22$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2+\sqrt{7}\right)^{2}.

$$3\left(4+4\sqrt{7}+\left(\sqrt{7}\right)^{2}\right)-12\left(2+\sqrt{7}\right)+13$$

The square of \sqrt{7} is 7.

$$3\left(4+4\sqrt{7}+7\right)-12\left(2+\sqrt{7}\right)+13$$

Add 4 and 7 to get 11.

$$3\left(11+4\sqrt{7}\right)-12\left(2+\sqrt{7}\right)+13$$

Use the distributive property to multiply 3 by 11+4\sqrt{7}.

$$33+12\sqrt{7}-12\left(2+\sqrt{7}\right)+13$$

Use the distributive property to multiply -12 by 2+\sqrt{7}.

$$33+12\sqrt{7}-24-12\sqrt{7}+13$$

Subtract 24 from 33 to get 9.

$$9+12\sqrt{7}-12\sqrt{7}+13$$

Combine 12\sqrt{7} and -12\sqrt{7} to get 0.

$$9+13$$

Add 9 and 13 to get 22.

$$22$$

Factor

$$2\times 11$$