Solve (3t-2)(3t+2)(9t^2+4)

$$( 3 t - 2 ) ( 3 t + 2 ) ( 9 t ^ { 2 } + 4 )$$

Evaluate

$$81t^{4}-16$$

Solution Steps

Use the distributive property to multiply 3t-2 by 3t+2 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$\left(9t^{2}\right)^{2}-16$$

Expand \left(9t^{2}\right)^{2}.

$$9^{2}\left(t^{2}\right)^{2}-16$$

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

$$9^{2}t^{4}-16$$

Calculate 9 to the power of 2 and get 81.

$$81t^{4}-16$$

Expand

$$81t^{4}-16$$

Solution Steps

Use the distributive property to multiply 3t-2 by 3t+2 and combine like terms.

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$\left(9t^{2}\right)^{2}-16$$

Expand \left(9t^{2}\right)^{2}.

$$9^{2}\left(t^{2}\right)^{2}-16$$

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

$$9^{2}t^{4}-16$$

Calculate 9 to the power of 2 and get 81.

$$81t^{4}-16$$