Solve (2a^3+5b)*(2a^3-5b)

$$( 2 a ^ { 3 } + 5 b ) \cdot ( 2 a ^ { 3 } - 5 b )$$

Evaluate

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

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}.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4a^{6}-\left(5b\right)^{2}$$

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

$$4a^{6}-5^{2}b^{2}$$

Calculate 5 to the power of 2 and get 25.

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

Expand

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

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}.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4a^{6}-\left(5b\right)^{2}$$

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

$$4a^{6}-5^{2}b^{2}$$

Calculate 5 to the power of 2 and get 25.

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