Solve 16(2a+1)(2a-1)(a^4+1/16)(4a^2+1)

$$16 ( 2 a + 1 ) ( 2 a - 1 ) ( a ^ { 4 } + \frac { 1 } { 16 } ) ( 4 a ^ { 2 } + 1 )$$

Evaluate

$$256a^{8}-1$$

Solution Steps

Use the distributive property to multiply 16 by 2a+1.

$$\left(32a+16\right)\left(2a-1\right)\left(a^{4}+\frac{1}{16}\right)\left(4a^{2}+1\right)$$

Use the distributive property to multiply 32a+16 by 2a-1 and combine like terms.

$$\left(64a^{2}-16\right)\left(a^{4}+\frac{1}{16}\right)\left(4a^{2}+1\right)$$

Use the distributive property to multiply 64a^{2}-16 by a^{4}+\frac{1}{16}.

$$\left(64a^{6}+4a^{2}-16a^{4}-1\right)\left(4a^{2}+1\right)$$

Use the distributive property to multiply 64a^{6}+4a^{2}-16a^{4}-1 by 4a^{2}+1 and combine like terms.

$$256a^{8}-1$$

Expand

$$256a^{8}-1$$

Solution Steps

Use the distributive property to multiply 16 by 2a+1.

$$\left(32a+16\right)\left(2a-1\right)\left(a^{4}+\frac{1}{16}\right)\left(4a^{2}+1\right)$$

Use the distributive property to multiply 32a+16 by 2a-1 and combine like terms.

$$\left(64a^{2}-16\right)\left(a^{4}+\frac{1}{16}\right)\left(4a^{2}+1\right)$$

Use the distributive property to multiply 64a^{2}-16 by a^{4}+\frac{1}{16}.

$$\left(64a^{6}+4a^{2}-16a^{4}-1\right)\left(4a^{2}+1\right)$$

Use the distributive property to multiply 64a^{6}+4a^{2}-16a^{4}-1 by 4a^{2}+1 and combine like terms.

$$256a^{8}-1$$