Solve (7e^4+5f^3)(7e^4-5f^3)=

$$( 7 e ^ { 4 } + 5 f ^ { 3 } ) ( 7 e ^ { 4 } - 5 f ^ { 3 } ) =$$

Evaluate

$$49e^{8}-25f^{6}$$

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}.

$$\left(7e^{4}\right)^{2}-\left(5f^{3}\right)^{2}$$

Expand \left(7e^{4}\right)^{2}.

$$7^{2}\left(e^{4}\right)^{2}-\left(5f^{3}\right)^{2}$$

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

$$7^{2}e^{8}-\left(5f^{3}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$49e^{8}-\left(5f^{3}\right)^{2}$$

Expand \left(5f^{3}\right)^{2}.

$$49e^{8}-5^{2}\left(f^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$49e^{8}-5^{2}f^{6}$$

Calculate 5 to the power of 2 and get 25.

$$49e^{8}-25f^{6}$$

Expand

$$49e^{8}-25f^{6}$$

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}.

$$\left(7e^{4}\right)^{2}-\left(5f^{3}\right)^{2}$$

Expand \left(7e^{4}\right)^{2}.

$$7^{2}\left(e^{4}\right)^{2}-\left(5f^{3}\right)^{2}$$

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

$$7^{2}e^{8}-\left(5f^{3}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$49e^{8}-\left(5f^{3}\right)^{2}$$

Expand \left(5f^{3}\right)^{2}.

$$49e^{8}-5^{2}\left(f^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$49e^{8}-5^{2}f^{6}$$

Calculate 5 to the power of 2 and get 25.

$$49e^{8}-25f^{6}$$