Solve =12[(1+frac{a_{0}+45}{a})^4/2-1]

$$= 12 [ ( 1 + \frac { a _ { 0 } + 45 } { a } ) ^ { 4 / 2 } - 1 ]$$

Evaluate

$$\frac{12\left(a_{0}+45\right)\left(2a+a_{0}+45\right)}{a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$12\left(\left(\frac{a}{a}+\frac{a_{0}+45}{a}\right)^{\frac{4}{2}}-1\right)$$

Since \frac{a}{a} and \frac{a_{0}+45}{a} have the same denominator, add them by adding their numerators.

$$12\left(\left(\frac{a+a_{0}+45}{a}\right)^{\frac{4}{2}}-1\right)$$

Divide 4 by 2 to get 2.

$$12\left(\left(\frac{a+a_{0}+45}{a}\right)^{2}-1\right)$$

To raise \frac{a+a_{0}+45}{a} to a power, raise both numerator and denominator to the power and then divide.

$$12\left(\frac{\left(a+a_{0}+45\right)^{2}}{a^{2}}-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a^{2}}{a^{2}}.

$$12\left(\frac{\left(a+a_{0}+45\right)^{2}}{a^{2}}-\frac{a^{2}}{a^{2}}\right)$$

Since \frac{\left(a+a_{0}+45\right)^{2}}{a^{2}} and \frac{a^{2}}{a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$12\times \frac{\left(a+a_{0}+45\right)^{2}-a^{2}}{a^{2}}$$

Do the multiplications in \left(a+a_{0}+45\right)^{2}-a^{2}.

$$12\times \frac{a^{2}+aa_{0}+45a+aa_{0}+a_{0}^{2}+45a_{0}+45a+45a_{0}+2025-a^{2}}{a^{2}}$$

Combine like terms in a^{2}+aa_{0}+45a+aa_{0}+a_{0}^{2}+45a_{0}+45a+45a_{0}+2025-a^{2}.

$$12\times \frac{2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025}{a^{2}}$$

Express 12\times \frac{2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025}{a^{2}} as a single fraction.

$$\frac{12\left(2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025\right)}{a^{2}}$$

Use the distributive property to multiply 12 by 2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025.

$$\frac{24aa_{0}+1080a+12a_{0}^{2}+1080a_{0}+24300}{a^{2}}$$

Expand

$$\frac{12\left(2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025\right)}{a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$12\left(\left(\frac{a}{a}+\frac{a_{0}+45}{a}\right)^{\frac{4}{2}}-1\right)$$

Since \frac{a}{a} and \frac{a_{0}+45}{a} have the same denominator, add them by adding their numerators.

$$12\left(\left(\frac{a+a_{0}+45}{a}\right)^{\frac{4}{2}}-1\right)$$

Divide 4 by 2 to get 2.

$$12\left(\left(\frac{a+a_{0}+45}{a}\right)^{2}-1\right)$$

To raise \frac{a+a_{0}+45}{a} to a power, raise both numerator and denominator to the power and then divide.

$$12\left(\frac{\left(a+a_{0}+45\right)^{2}}{a^{2}}-1\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a^{2}}{a^{2}}.

$$12\left(\frac{\left(a+a_{0}+45\right)^{2}}{a^{2}}-\frac{a^{2}}{a^{2}}\right)$$

Since \frac{\left(a+a_{0}+45\right)^{2}}{a^{2}} and \frac{a^{2}}{a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$12\times \frac{\left(a+a_{0}+45\right)^{2}-a^{2}}{a^{2}}$$

Do the multiplications in \left(a+a_{0}+45\right)^{2}-a^{2}.

$$12\times \frac{a^{2}+aa_{0}+45a+aa_{0}+a_{0}^{2}+45a_{0}+45a+45a_{0}+2025-a^{2}}{a^{2}}$$

Combine like terms in a^{2}+aa_{0}+45a+aa_{0}+a_{0}^{2}+45a_{0}+45a+45a_{0}+2025-a^{2}.

$$12\times \frac{2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025}{a^{2}}$$

Express 12\times \frac{2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025}{a^{2}} as a single fraction.

$$\frac{12\left(2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025\right)}{a^{2}}$$

Use the distributive property to multiply 12 by 2aa_{0}+90a+a_{0}^{2}+90a_{0}+2025.

$$\frac{24aa_{0}+1080a+12a_{0}^{2}+1080a_{0}+24300}{a^{2}}$$