Solve (2x^{3}-y^{3})(2x^3+y^3)(4x^6+y^6)

$$( 2 x ^ { 3 } - y ^ { 3 } ) ( 2 x ^ { 3 } + y ^ { 3 } ) ( 4 x ^ { 6 } + y ^ { 6 } )$$

Evaluate

$$16x^{12}-y^{12}$$

Solution Steps

Use the distributive property to multiply 2x^{3}-y^{3} by 2x^{3}+y^{3} and combine like terms.

$$\left(4x^{6}-y^{6}\right)\left(4x^{6}+y^{6}\right)$$

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

$$\left(4x^{6}\right)^{2}-\left(y^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(4x^{6}\right)^{2}-y^{12}$$

Expand \left(4x^{6}\right)^{2}.

$$4^{2}\left(x^{6}\right)^{2}-y^{12}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$4^{2}x^{12}-y^{12}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{12}-y^{12}$$

Expand

$$16x^{12}-y^{12}$$

Solution Steps

Use the distributive property to multiply 2x^{3}-y^{3} by 2x^{3}+y^{3} and combine like terms.

$$\left(4x^{6}-y^{6}\right)\left(4x^{6}+y^{6}\right)$$

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

$$\left(4x^{6}\right)^{2}-\left(y^{6}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(4x^{6}\right)^{2}-y^{12}$$

Expand \left(4x^{6}\right)^{2}.

$$4^{2}\left(x^{6}\right)^{2}-y^{12}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$4^{2}x^{12}-y^{12}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{12}-y^{12}$$