Solve 05(sqrt{y^2+10}+y)(sqrt{y^2+10}+y)-2

$$05( \sqrt{ { y }^{ 2 } +10 } +y)( \sqrt{ { y }^{ 2 } +10 } +y)-2$$

Evaluate

$$-2$$

Solution Steps

Multiply \sqrt{y^{2}+10}+y and \sqrt{y^{2}+10}+y to get \left(\sqrt{y^{2}+10}+y\right)^{2}.

$$0\times 5\left(\sqrt{y^{2}+10}+y\right)^{2}-2$$

Multiply 0 and 5 to get 0.

$$0\left(\sqrt{y^{2}+10}+y\right)^{2}-2$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{y^{2}+10}+y\right)^{2}.

$$0\left(\left(\sqrt{y^{2}+10}\right)^{2}+2\sqrt{y^{2}+10}y+y^{2}\right)-2$$

Calculate \sqrt{y^{2}+10} to the power of 2 and get y^{2}+10.

$$0\left(y^{2}+10+2\sqrt{y^{2}+10}y+y^{2}\right)-2$$

Combine y^{2} and y^{2} to get 2y^{2}.

$$0\left(2y^{2}+10+2\sqrt{y^{2}+10}y\right)-2$$

Use the distributive property to multiply 0 by 2y^{2}+10+2\sqrt{y^{2}+10}y and combine like terms.

$$3\times 0-2$$

Multiply 3 and 0 to get 0.

$$0-2$$

Subtract 2 from 0 to get -2.

$$-2$$

Factor

$$-2$$