Solve (2x-1)(2x+1)(4x^2+1)

$$( 2 x - 1 ) ( 2 x + 1 ) ( 4 x ^ { 2 } + 1 )$$

Evaluate

$$16x^{4}-1$$

Solution Steps

Use the distributive property to multiply 2x-1 by 2x+1 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

Expand \left(4x^{2}\right)^{2}.

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

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

$$4^{2}x^{4}-1$$

Calculate 4 to the power of 2 and get 16.

$$16x^{4}-1$$

Expand

$$16x^{4}-1$$

Solution Steps

Use the distributive property to multiply 2x-1 by 2x+1 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

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

Expand \left(4x^{2}\right)^{2}.

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

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

$$4^{2}x^{4}-1$$

Calculate 4 to the power of 2 and get 16.

$$16x^{4}-1$$