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

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

Evaluate

$$25a^{4}-9b^{2}$$

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}.

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

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

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

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

$$5^{2}a^{4}-\left(3b\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25a^{4}-\left(3b\right)^{2}$$

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

$$25a^{4}-3^{2}b^{2}$$

Calculate 3 to the power of 2 and get 9.

$$25a^{4}-9b^{2}$$

Expand

$$25a^{4}-9b^{2}$$

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}.

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

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

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

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

$$5^{2}a^{4}-\left(3b\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25a^{4}-\left(3b\right)^{2}$$

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

$$25a^{4}-3^{2}b^{2}$$

Calculate 3 to the power of 2 and get 9.

$$25a^{4}-9b^{2}$$