Solve (5a^3-6a^2)(5a^3+6a^2)=

$$( 5 a ^ { 3 } - 6 a ^ { 2 } ) ( 5 a ^ { 3 } + 6 a ^ { 2 } ) =$$

Evaluate

$$\left(25a^{2}-36\right)a^{4}$$

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}.

$$\left(5a^{3}\right)^{2}-\left(6a^{2}\right)^{2}$$

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

$$5^{2}\left(a^{3}\right)^{2}-\left(6a^{2}\right)^{2}$$

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

$$5^{2}a^{6}-\left(6a^{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25a^{6}-\left(6a^{2}\right)^{2}$$

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

$$25a^{6}-6^{2}\left(a^{2}\right)^{2}$$

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

$$25a^{6}-6^{2}a^{4}$$

Calculate 6 to the power of 2 and get 36.

$$25a^{6}-36a^{4}$$

Expand

$$25a^{6}-36a^{4}$$

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}.

$$\left(5a^{3}\right)^{2}-\left(6a^{2}\right)^{2}$$

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

$$5^{2}\left(a^{3}\right)^{2}-\left(6a^{2}\right)^{2}$$

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

$$5^{2}a^{6}-\left(6a^{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25a^{6}-\left(6a^{2}\right)^{2}$$

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

$$25a^{6}-6^{2}\left(a^{2}\right)^{2}$$

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

$$25a^{6}-6^{2}a^{4}$$

Calculate 6 to the power of 2 and get 36.

$$25a^{6}-36a^{4}$$