Solve (7x^6+4x^4)*(7x^6-4x^4)=

$$( 7 x ^ { 6 } + 4 x ^ { 4 } ) \cdot ( 7 x ^ { 6 } - 4 x ^ { 4 } ) =$$

Evaluate

$$\left(49x^{4}-16\right)x^{8}$$

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}.

$$\left(7x^{6}\right)^{2}-\left(4x^{4}\right)^{2}$$

Expand \left(7x^{6}\right)^{2}.

$$7^{2}\left(x^{6}\right)^{2}-\left(4x^{4}\right)^{2}$$

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

$$7^{2}x^{12}-\left(4x^{4}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$49x^{12}-\left(4x^{4}\right)^{2}$$

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

$$49x^{12}-4^{2}\left(x^{4}\right)^{2}$$

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

$$49x^{12}-4^{2}x^{8}$$

Calculate 4 to the power of 2 and get 16.

$$49x^{12}-16x^{8}$$

Expand

$$49x^{12}-16x^{8}$$

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}.

$$\left(7x^{6}\right)^{2}-\left(4x^{4}\right)^{2}$$

Expand \left(7x^{6}\right)^{2}.

$$7^{2}\left(x^{6}\right)^{2}-\left(4x^{4}\right)^{2}$$

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

$$7^{2}x^{12}-\left(4x^{4}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$49x^{12}-\left(4x^{4}\right)^{2}$$

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

$$49x^{12}-4^{2}\left(x^{4}\right)^{2}$$

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

$$49x^{12}-4^{2}x^{8}$$

Calculate 4 to the power of 2 and get 16.

$$49x^{12}-16x^{8}$$