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

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

Evaluate

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

Solution Steps

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

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

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.

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

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

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

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

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

Calculate 4 to the power of 2 and get 16.

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

Expand

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

Solution Steps

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

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

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.

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

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

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

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

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

Calculate 4 to the power of 2 and get 16.

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