Solve (2x-a)(2x+a)(4x^2+a^2)(16x^4+a^4)

$$( 2 x - a ) ( 2 x + a ) ( 4 x ^ { 2 } + a ^ { 2 } ) ( 16 x ^ { 4 } + a ^ { 4 } )$$

Evaluate

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

Solution Steps

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

$$\left(4x^{2}-a^{2}\right)\left(4x^{2}+a^{2}\right)\left(16x^{4}+a^{4}\right)$$

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

$$\left(16x^{4}-a^{4}\right)\left(16x^{4}+a^{4}\right)$$

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

$$\left(16x^{4}\right)^{2}-\left(a^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(16x^{4}\right)^{2}-a^{8}$$

Expand \left(16x^{4}\right)^{2}.

$$16^{2}\left(x^{4}\right)^{2}-a^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$16^{2}x^{8}-a^{8}$$

Calculate 16 to the power of 2 and get 256.

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

Expand

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

Solution Steps

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

$$\left(4x^{2}-a^{2}\right)\left(4x^{2}+a^{2}\right)\left(16x^{4}+a^{4}\right)$$

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

$$\left(16x^{4}-a^{4}\right)\left(16x^{4}+a^{4}\right)$$

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

$$\left(16x^{4}\right)^{2}-\left(a^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\left(16x^{4}\right)^{2}-a^{8}$$

Expand \left(16x^{4}\right)^{2}.

$$16^{2}\left(x^{4}\right)^{2}-a^{8}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$16^{2}x^{8}-a^{8}$$

Calculate 16 to the power of 2 and get 256.

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