Solve (3r^2+5t^2)(3r^2-5t^2)

$$( 3 r ^ { 2 } + 5 t ^ { 2 } ) ( 3 r ^ { 2 } - 5 t ^ { 2 } )$$

Evaluate

$$9r^{4}-25t^{4}$$

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}.

$$\left(3r^{2}\right)^{2}-\left(5t^{2}\right)^{2}$$

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

$$3^{2}\left(r^{2}\right)^{2}-\left(5t^{2}\right)^{2}$$

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

$$3^{2}r^{4}-\left(5t^{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9r^{4}-\left(5t^{2}\right)^{2}$$

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

$$9r^{4}-5^{2}\left(t^{2}\right)^{2}$$

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

$$9r^{4}-5^{2}t^{4}$$

Calculate 5 to the power of 2 and get 25.

$$9r^{4}-25t^{4}$$

Expand

$$9r^{4}-25t^{4}$$

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}.

$$\left(3r^{2}\right)^{2}-\left(5t^{2}\right)^{2}$$

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

$$3^{2}\left(r^{2}\right)^{2}-\left(5t^{2}\right)^{2}$$

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

$$3^{2}r^{4}-\left(5t^{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9r^{4}-\left(5t^{2}\right)^{2}$$

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

$$9r^{4}-5^{2}\left(t^{2}\right)^{2}$$

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

$$9r^{4}-5^{2}t^{4}$$

Calculate 5 to the power of 2 and get 25.

$$9r^{4}-25t^{4}$$