Solve {left(16+8x+2x^2/2+xright)}^2-4

$${ \left( \frac{ 16+8x+2 { x }^{ 2 } }{ 2+x } \right) }^{ 2 } -4$$

Evaluate

$$\frac{4\left(x^{2}+3x+6\right)\left(x^{2}+5x+10\right)}{\left(x+2\right)^{2}}$$

Short Solution Steps

To raise \frac{16+8x+2x^{2}}{2+x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(16+8x+2x^{2}\right)^{2}}{\left(2+x\right)^{2}}-4$$

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

$$\frac{\left(16+8x+2x^{2}\right)^{2}}{\left(2+x\right)^{2}}-\frac{4\left(2+x\right)^{2}}{\left(2+x\right)^{2}}$$

Since \frac{\left(16+8x+2x^{2}\right)^{2}}{\left(2+x\right)^{2}} and \frac{4\left(2+x\right)^{2}}{\left(2+x\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(16+8x+2x^{2}\right)^{2}-4\left(2+x\right)^{2}}{\left(2+x\right)^{2}}$$

Do the multiplications in \left(16+8x+2x^{2}\right)^{2}-4\left(2+x\right)^{2}.

$$\frac{256+128x+32x^{2}+128x+64x^{2}+16x^{3}+32x^{2}+16x^{3}+4x^{4}-16-16x-4x^{2}}{\left(2+x\right)^{2}}$$

Combine like terms in 256+128x+32x^{2}+128x+64x^{2}+16x^{3}+32x^{2}+16x^{3}+4x^{4}-16-16x-4x^{2}.

$$\frac{240+240x+124x^{2}+32x^{3}+4x^{4}}{\left(2+x\right)^{2}}$$

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

$$\frac{240+240x+124x^{2}+32x^{3}+4x^{4}}{x^{2}+4x+4}$$

Expand

$$\frac{4\left(x^{4}+8x^{3}+31x^{2}+60x+60\right)}{\left(x+2\right)^{2}}$$

Short Solution Steps

To raise \frac{16+8x+2x^{2}}{2+x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(16+8x+2x^{2}\right)^{2}}{\left(2+x\right)^{2}}-4$$

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

$$\frac{\left(16+8x+2x^{2}\right)^{2}}{\left(2+x\right)^{2}}-\frac{4\left(2+x\right)^{2}}{\left(2+x\right)^{2}}$$

Since \frac{\left(16+8x+2x^{2}\right)^{2}}{\left(2+x\right)^{2}} and \frac{4\left(2+x\right)^{2}}{\left(2+x\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(16+8x+2x^{2}\right)^{2}-4\left(2+x\right)^{2}}{\left(2+x\right)^{2}}$$

Do the multiplications in \left(16+8x+2x^{2}\right)^{2}-4\left(2+x\right)^{2}.

$$\frac{256+128x+32x^{2}+128x+64x^{2}+16x^{3}+32x^{2}+16x^{3}+4x^{4}-16-16x-4x^{2}}{\left(2+x\right)^{2}}$$

Combine like terms in 256+128x+32x^{2}+128x+64x^{2}+16x^{3}+32x^{2}+16x^{3}+4x^{4}-16-16x-4x^{2}.

$$\frac{240+240x+124x^{2}+32x^{3}+4x^{4}}{\left(2+x\right)^{2}}$$

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

$$\frac{240+240x+124x^{2}+32x^{3}+4x^{4}}{x^{2}+4x+4}$$