Solve =(2x^2+1)^2+3(2x^2+1)

$$= ( 2 x ^ { 2 } + 1 ) ^ { 2 } + 3 ( 2 x ^ { 2 } + 1 )$$

Evaluate

$$4x^{4}+10x^{2}+4$$

Solution Steps

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

$$4\left(x^{2}\right)^{2}+4x^{2}+1+3\left(2x^{2}+1\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$4x^{4}+4x^{2}+1+3\left(2x^{2}+1\right)$$

Use the distributive property to multiply 3 by 2x^{2}+1.

$$4x^{4}+4x^{2}+1+6x^{2}+3$$

Combine 4x^{2} and 6x^{2} to get 10x^{2}.

$$4x^{4}+10x^{2}+1+3$$

Add 1 and 3 to get 4.

$$4x^{4}+10x^{2}+4$$

Expand

$$4x^{4}+10x^{2}+4$$

Solution Steps

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

$$4\left(x^{2}\right)^{2}+4x^{2}+1+3\left(2x^{2}+1\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$4x^{4}+4x^{2}+1+3\left(2x^{2}+1\right)$$

Use the distributive property to multiply 3 by 2x^{2}+1.

$$4x^{4}+4x^{2}+1+6x^{2}+3$$

Combine 4x^{2} and 6x^{2} to get 10x^{2}.

$$4x^{4}+10x^{2}+1+3$$

Add 1 and 3 to get 4.

$$4x^{4}+10x^{2}+4$$