Solve {left(2x+1/2right)}^2*2

$${ \left(2x+ \frac{ 1 }{ 2 } \right) }^{ 2 } \times 2$$

Evaluate

$$\frac{\left(4x+1\right)^{2}}{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+\frac{1}{2}\right)^{2}.

$$\left(4x^{2}+2x+\frac{1}{4}\right)\times 2$$

Use the distributive property to multiply 4x^{2}+2x+\frac{1}{4} by 2.

$$8x^{2}+4x+\frac{1}{2}$$

Expand

$$8x^{2}+4x+\frac{1}{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+\frac{1}{2}\right)^{2}.

$$\left(4x^{2}+2x+\frac{1}{4}\right)\times 2$$

Use the distributive property to multiply 4x^{2}+2x+\frac{1}{4} by 2.

$$8x^{2}+4x+\frac{1}{2}$$