Solve 5^2+4*5*(sqrt{5}-2)+5*(sqrt{5}-2)^2

$$5 ^ { 2 } + 4 \cdot 5 \cdot ( \sqrt { 5 } - 2 ) + 5 \cdot ( \sqrt { 5 } - 2 ) ^ { 2 }$$

Evaluate

$$30$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$25+4\times 5\left(\sqrt{5}-2\right)+5\left(\sqrt{5}-2\right)^{2}$$

Multiply 4 and 5 to get 20.

$$25+20\left(\sqrt{5}-2\right)+5\left(\sqrt{5}-2\right)^{2}$$

Use the distributive property to multiply 20 by \sqrt{5}-2.

$$25+20\sqrt{5}-40+5\left(\sqrt{5}-2\right)^{2}$$

Subtract 40 from 25 to get -15.

$$-15+20\sqrt{5}+5\left(\sqrt{5}-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{5}-2\right)^{2}.

$$-15+20\sqrt{5}+5\left(\left(\sqrt{5}\right)^{2}-4\sqrt{5}+4\right)$$

The square of \sqrt{5} is 5.

$$-15+20\sqrt{5}+5\left(5-4\sqrt{5}+4\right)$$

Add 5 and 4 to get 9.

$$-15+20\sqrt{5}+5\left(9-4\sqrt{5}\right)$$

Use the distributive property to multiply 5 by 9-4\sqrt{5}.

$$-15+20\sqrt{5}+45-20\sqrt{5}$$

Add -15 and 45 to get 30.

$$30+20\sqrt{5}-20\sqrt{5}$$

Combine 20\sqrt{5} and -20\sqrt{5} to get 0.

$$30$$

Factor

$$2\times 3\times 5$$