Solve (6a^4-7b^3)(6a^4+7b^3)

$$( 6 a ^ { 4 } - 7 b ^ { 3 } ) ( 6 a ^ { 4 } + 7 b ^ { 3 } )$$

Evaluate

$$36a^{8}-49b^{6}$$

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}.

$$\left(6a^{4}\right)^{2}-\left(7b^{3}\right)^{2}$$

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

$$6^{2}\left(a^{4}\right)^{2}-\left(7b^{3}\right)^{2}$$

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

$$6^{2}a^{8}-\left(7b^{3}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36a^{8}-\left(7b^{3}\right)^{2}$$

Expand \left(7b^{3}\right)^{2}.

$$36a^{8}-7^{2}\left(b^{3}\right)^{2}$$

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

$$36a^{8}-7^{2}b^{6}$$

Calculate 7 to the power of 2 and get 49.

$$36a^{8}-49b^{6}$$

Expand

$$36a^{8}-49b^{6}$$

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}.

$$\left(6a^{4}\right)^{2}-\left(7b^{3}\right)^{2}$$

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

$$6^{2}\left(a^{4}\right)^{2}-\left(7b^{3}\right)^{2}$$

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

$$6^{2}a^{8}-\left(7b^{3}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36a^{8}-\left(7b^{3}\right)^{2}$$

Expand \left(7b^{3}\right)^{2}.

$$36a^{8}-7^{2}\left(b^{3}\right)^{2}$$

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

$$36a^{8}-7^{2}b^{6}$$

Calculate 7 to the power of 2 and get 49.

$$36a^{8}-49b^{6}$$