Solve {left(5+1/2right)}^2+5+1/25-1/2+{left(5-1/2right)}^2

$${ \left( \frac{ 5+1 }{ 2 } \right) }^{ 2 } + \frac{ 5+1 }{ 2 } \frac{ 5-1 }{ 2 } + { \left( \frac{ 5-1 }{ 2 } \right) }^{ 2 }$$

Evaluate

$$19$$

Solution Steps

Add 5 and 1 to get 6.

$$\left(\frac{6}{2}\right)^{2}+\frac{5+1}{2}\times \frac{5-1}{2}+\left(\frac{5-1}{2}\right)^{2}$$

Divide 6 by 2 to get 3.

$$3^{2}+\frac{5+1}{2}\times \frac{5-1}{2}+\left(\frac{5-1}{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9+\frac{5+1}{2}\times \frac{5-1}{2}+\left(\frac{5-1}{2}\right)^{2}$$

Add 5 and 1 to get 6.

$$9+\frac{6}{2}\times \frac{5-1}{2}+\left(\frac{5-1}{2}\right)^{2}$$

Divide 6 by 2 to get 3.

$$9+3\times \frac{5-1}{2}+\left(\frac{5-1}{2}\right)^{2}$$

Subtract 1 from 5 to get 4.

$$9+3\times \frac{4}{2}+\left(\frac{5-1}{2}\right)^{2}$$

Divide 4 by 2 to get 2.

$$9+3\times 2+\left(\frac{5-1}{2}\right)^{2}$$

Multiply 3 and 2 to get 6.

$$9+6+\left(\frac{5-1}{2}\right)^{2}$$

Add 9 and 6 to get 15.

$$15+\left(\frac{5-1}{2}\right)^{2}$$

Subtract 1 from 5 to get 4.

$$15+\left(\frac{4}{2}\right)^{2}$$

Divide 4 by 2 to get 2.

$$15+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$15+4$$

Add 15 and 4 to get 19.

$$19$$

Factor

$$19$$