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

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

Evaluate

$$9\left(x^{4}-4y^{8}\right)$$

Solution Steps

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

$$\left(3x^{2}\right)^{2}-\left(6y^{4}\right)^{2}$$

Expand \left(3x^{2}\right)^{2}.

$$3^{2}\left(x^{2}\right)^{2}-\left(6y^{4}\right)^{2}$$

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

$$3^{2}x^{4}-\left(6y^{4}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}-\left(6y^{4}\right)^{2}$$

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

$$9x^{4}-6^{2}\left(y^{4}\right)^{2}$$

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

$$9x^{4}-6^{2}y^{8}$$

Calculate 6 to the power of 2 and get 36.

$$9x^{4}-36y^{8}$$

Expand

$$9x^{4}-36y^{8}$$

Solution Steps

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

$$\left(3x^{2}\right)^{2}-\left(6y^{4}\right)^{2}$$

Expand \left(3x^{2}\right)^{2}.

$$3^{2}\left(x^{2}\right)^{2}-\left(6y^{4}\right)^{2}$$

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

$$3^{2}x^{4}-\left(6y^{4}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}-\left(6y^{4}\right)^{2}$$

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

$$9x^{4}-6^{2}\left(y^{4}\right)^{2}$$

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

$$9x^{4}-6^{2}y^{8}$$

Calculate 6 to the power of 2 and get 36.

$$9x^{4}-36y^{8}$$