Solve (-6c-3a/4)^2-4ac

$$( \frac { - 6 c - 3 a } { 4 } ) ^ { 2 } - 4 a c$$

Evaluate

$$\frac{9\left(a+2c\right)^{2}}{16}-4ac$$

Short Solution Steps

To raise \frac{-6c-3a}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-6c-3a\right)^{2}}{4^{2}}-4ac$$

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

$$\frac{\left(-6c-3a\right)^{2}}{4^{2}}+\frac{-4ac\times 4^{2}}{4^{2}}$$

Since \frac{\left(-6c-3a\right)^{2}}{4^{2}} and \frac{-4ac\times 4^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-6c-3a\right)^{2}-4ac\times 4^{2}}{4^{2}}$$

Do the multiplications in \left(-6c-3a\right)^{2}-4ac\times 4^{2}.

$$\frac{36c^{2}+36ca+9a^{2}-64ac}{4^{2}}$$

Combine like terms in 36c^{2}+36ca+9a^{2}-64ac.

$$\frac{36c^{2}+9a^{2}-28ca}{4^{2}}$$

Expand 4^{2}.

$$\frac{36c^{2}+9a^{2}-28ca}{16}$$

Expand

$$-\frac{7ac}{4}+\frac{9a^{2}}{16}+\frac{9c^{2}}{4}$$

Short Solution Steps

To raise \frac{-6c-3a}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-6c-3a\right)^{2}}{4^{2}}-4ac$$

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

$$\frac{\left(-6c-3a\right)^{2}}{4^{2}}+\frac{-4ac\times 4^{2}}{4^{2}}$$

Since \frac{\left(-6c-3a\right)^{2}}{4^{2}} and \frac{-4ac\times 4^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-6c-3a\right)^{2}-4ac\times 4^{2}}{4^{2}}$$

Do the multiplications in \left(-6c-3a\right)^{2}-4ac\times 4^{2}.

$$\frac{36c^{2}+36ca+9a^{2}-64ac}{4^{2}}$$

Combine like terms in 36c^{2}+36ca+9a^{2}-64ac.

$$\frac{36c^{2}+9a^{2}-28ca}{4^{2}}$$

Expand 4^{2}.

$$\frac{36c^{2}+9a^{2}-28ca}{16}$$