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

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

Evaluate

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

Solution Steps

Multiply 2x^{2}+1 and 2x^{2}+1 to get \left(2x^{2}+1\right)^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x^{2}+1\right)^{3}.

$$8\left(x^{2}\right)^{3}+12\left(x^{2}\right)^{2}+6x^{2}+1$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$8x^{6}+12\left(x^{2}\right)^{2}+6x^{2}+1$$

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

$$8x^{6}+12x^{4}+6x^{2}+1$$

Expand

$$8x^{6}+12x^{4}+6x^{2}+1$$

Solution Steps

Multiply 2x^{2}+1 and 2x^{2}+1 to get \left(2x^{2}+1\right)^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(2x^{2}+1\right)^{3}.

$$8\left(x^{2}\right)^{3}+12\left(x^{2}\right)^{2}+6x^{2}+1$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$8x^{6}+12\left(x^{2}\right)^{2}+6x^{2}+1$$

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

$$8x^{6}+12x^{4}+6x^{2}+1$$