Solve (3/2m+3)^2-16

$$( \frac { 3 } { 2 m + 3 } ) ^ { 2 } - 16$$

Evaluate

$$-\frac{\left(8m+9\right)\left(8m+15\right)}{\left(2m+3\right)^{2}}$$

Short Solution Steps

To raise \frac{3}{2m+3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{3^{2}}{\left(2m+3\right)^{2}}-16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}}.

$$\frac{3^{2}}{\left(2m+3\right)^{2}}-\frac{16\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}}$$

Since \frac{3^{2}}{\left(2m+3\right)^{2}} and \frac{16\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3^{2}-16\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}}$$

Do the multiplications in 3^{2}-16\left(2m+3\right)^{2}.

$$\frac{3^{2}-64m^{2}-192m-144}{\left(2m+3\right)^{2}}$$

Combine like terms in 3^{2}-64m^{2}-192m-144.

$$\frac{-135-64m^{2}-192m}{\left(2m+3\right)^{2}}$$

Expand \left(2m+3\right)^{2}.

$$\frac{-135-64m^{2}-192m}{4m^{2}+12m+9}$$

Expand

$$-\frac{64m^{2}+192m+135}{\left(2m+3\right)^{2}}$$

Short Solution Steps

To raise \frac{3}{2m+3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{3^{2}}{\left(2m+3\right)^{2}}-16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}}.

$$\frac{3^{2}}{\left(2m+3\right)^{2}}-\frac{16\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}}$$

Since \frac{3^{2}}{\left(2m+3\right)^{2}} and \frac{16\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3^{2}-16\left(2m+3\right)^{2}}{\left(2m+3\right)^{2}}$$

Do the multiplications in 3^{2}-16\left(2m+3\right)^{2}.

$$\frac{3^{2}-64m^{2}-192m-144}{\left(2m+3\right)^{2}}$$

Combine like terms in 3^{2}-64m^{2}-192m-144.

$$\frac{-135-64m^{2}-192m}{\left(2m+3\right)^{2}}$$

Expand \left(2m+3\right)^{2}.

$$\frac{-135-64m^{2}-192m}{4m^{2}+12m+9}$$