Solve 4x^2+16{left(9-2x/4right)}^2

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

Evaluate

$$8x^{2}-36x+81$$

Short Solution Steps

To raise \frac{9-2x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$4x^{2}+16\times \frac{\left(9-2x\right)^{2}}{4^{2}}$$

Express 16\times \frac{\left(9-2x\right)^{2}}{4^{2}} as a single fraction.

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

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

$$\frac{4x^{2}\times 4^{2}}{4^{2}}+\frac{16\left(9-2x\right)^{2}}{4^{2}}$$

Since \frac{4x^{2}\times 4^{2}}{4^{2}} and \frac{16\left(9-2x\right)^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4x^{2}\times 4^{2}+16\left(9-2x\right)^{2}}{4^{2}}$$

Do the multiplications in 4x^{2}\times 4^{2}+16\left(9-2x\right)^{2}.

$$\frac{64x^{2}+1296-576x+64x^{2}}{4^{2}}$$

Combine like terms in 64x^{2}+1296-576x+64x^{2}.

$$\frac{128x^{2}+1296-576x}{4^{2}}$$

Expand 4^{2}.

$$\frac{128x^{2}+1296-576x}{16}$$

Divide each term of 128x^{2}+1296-576x by 16 to get 8x^{2}+81-36x.

$$8x^{2}+81-36x$$

Expand

$$8x^{2}-36x+81$$

Short Solution Steps

To raise \frac{9-2x}{4} to a power, raise both numerator and denominator to the power and then divide.

$$4x^{2}+16\times \frac{\left(9-2x\right)^{2}}{4^{2}}$$

Express 16\times \frac{\left(9-2x\right)^{2}}{4^{2}} as a single fraction.

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

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

$$\frac{4x^{2}\times 4^{2}}{4^{2}}+\frac{16\left(9-2x\right)^{2}}{4^{2}}$$

Since \frac{4x^{2}\times 4^{2}}{4^{2}} and \frac{16\left(9-2x\right)^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{4x^{2}\times 4^{2}+16\left(9-2x\right)^{2}}{4^{2}}$$

Do the multiplications in 4x^{2}\times 4^{2}+16\left(9-2x\right)^{2}.

$$\frac{64x^{2}+1296-576x+64x^{2}}{4^{2}}$$

Combine like terms in 64x^{2}+1296-576x+64x^{2}.

$$\frac{128x^{2}+1296-576x}{4^{2}}$$

Expand 4^{2}.

$$\frac{128x^{2}+1296-576x}{16}$$

Divide each term of 128x^{2}+1296-576x by 16 to get 8x^{2}+81-36x.

$$8x^{2}+81-36x$$