Solve (sqrt{11}-1)*(sqrt{11}-1)+2*(sqrt{11}-1)

$$( \sqrt{ 11 } -1) \times ( \sqrt{ 11 } -1)+2 \times ( \sqrt{ 11 } -1)$$

Evaluate

$$10$$

Solution Steps

Multiply \sqrt{11}-1 and \sqrt{11}-1 to get \left(\sqrt{11}-1\right)^{2}.

$$\left(\sqrt{11}-1\right)^{2}+2\left(\sqrt{11}-1\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{11}-1\right)^{2}.

$$\left(\sqrt{11}\right)^{2}-2\sqrt{11}+1+2\left(\sqrt{11}-1\right)$$

The square of \sqrt{11} is 11.

$$11-2\sqrt{11}+1+2\left(\sqrt{11}-1\right)$$

Add 11 and 1 to get 12.

$$12-2\sqrt{11}+2\left(\sqrt{11}-1\right)$$

Use the distributive property to multiply 2 by \sqrt{11}-1.

$$12-2\sqrt{11}+2\sqrt{11}-2$$

Combine -2\sqrt{11} and 2\sqrt{11} to get 0.

$$12-2$$

Subtract 2 from 12 to get 10.

$$10$$

Factor

$$2\times 5$$