Solve 4a^2+1/4a^2-2+4a-1/2

$$4 a ^ { 2 } + \frac { 1 } { 4 a ^ { 2 } } - 2 + 4 a - \frac { 1 } { 2 }$$

Evaluate

$$4a^{2}+4a-\frac{5}{2}+\frac{1}{4a^{2}}$$

Short Solution Steps

Subtract \frac{1}{2} from -2 to get -\frac{5}{2}.

$$4a^{2}+\frac{1}{4a^{2}}-\frac{5}{2}+4a$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4a^{2} and 2 is 4a^{2}. Multiply \frac{5}{2} times \frac{2a^{2}}{2a^{2}}.

$$4a^{2}+\frac{1}{4a^{2}}-\frac{5\times 2a^{2}}{4a^{2}}+4a$$

Since \frac{1}{4a^{2}} and \frac{5\times 2a^{2}}{4a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$4a^{2}+\frac{1-5\times 2a^{2}}{4a^{2}}+4a$$

Do the multiplications in 1-5\times 2a^{2}.

$$4a^{2}+\frac{1-10a^{2}}{4a^{2}}+4a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4a times \frac{4a^{2}}{4a^{2}}.

$$4a^{2}+\frac{1-10a^{2}}{4a^{2}}+\frac{4a\times 4a^{2}}{4a^{2}}$$

Since \frac{1-10a^{2}}{4a^{2}} and \frac{4a\times 4a^{2}}{4a^{2}} have the same denominator, add them by adding their numerators.

$$4a^{2}+\frac{1-10a^{2}+4a\times 4a^{2}}{4a^{2}}$$

Do the multiplications in 1-10a^{2}+4a\times 4a^{2}.

$$4a^{2}+\frac{1-10a^{2}+16a^{3}}{4a^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4a^{2} times \frac{4a^{2}}{4a^{2}}.

$$\frac{4a^{2}\times 4a^{2}}{4a^{2}}+\frac{1-10a^{2}+16a^{3}}{4a^{2}}$$

Since \frac{4a^{2}\times 4a^{2}}{4a^{2}} and \frac{1-10a^{2}+16a^{3}}{4a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4a^{2}\times 4a^{2}+1-10a^{2}+16a^{3}}{4a^{2}}$$

Do the multiplications in 4a^{2}\times 4a^{2}+1-10a^{2}+16a^{3}.

$$\frac{16a^{4}+1-10a^{2}+16a^{3}}{4a^{2}}$$

Factor

$$\frac{16a^{4}+16a^{3}-10a^{2}+1}{4a^{2}}$$