Solve (2a+1)(2a-1)(9a^2+3)-(-6a^2)^2-(12a^3-8a):(4a)

$$( 2 a + 1 ) ( 2 a - 1 ) ( 9 a ^ { 2 } + 3 ) - ( - 6 a ^ { 2 } ) ^ { 2 } - ( 12 a ^ { 3 } - 8 a ) : ( 4 a )$$

Evaluate

$$-1$$

Short Solution Steps

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

$$\left(2a+1\right)\left(2a-1\right)\left(9a^{2}+3\right)-\left(-6\right)^{2}\left(a^{2}\right)^{2}-\frac{12a^{3}-8a}{4a}$$

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

$$\left(2a+1\right)\left(2a-1\right)\left(9a^{2}+3\right)-\left(-6\right)^{2}a^{4}-\frac{12a^{3}-8a}{4a}$$

Calculate -6 to the power of 2 and get 36.

$$\left(2a+1\right)\left(2a-1\right)\left(9a^{2}+3\right)-36a^{4}-\frac{12a^{3}-8a}{4a}$$

Factor the expressions that are not already factored in \frac{12a^{3}-8a}{4a}.

$$\left(2a+1\right)\left(2a-1\right)\left(9a^{2}+3\right)-36a^{4}-\frac{4a\left(3a^{2}-2\right)}{4a}$$

Cancel out 4a in both numerator and denominator.

$$\left(2a+1\right)\left(2a-1\right)\left(9a^{2}+3\right)-36a^{4}-\left(3a^{2}-2\right)$$

To find the opposite of 3a^{2}-2, find the opposite of each term.

$$\left(2a+1\right)\left(2a-1\right)\left(9a^{2}+3\right)-36a^{4}-3a^{2}+2$$

Use the distributive property to multiply 2a+1 by 2a-1 and combine like terms.

$$\left(4a^{2}-1\right)\left(9a^{2}+3\right)-36a^{4}-3a^{2}+2$$

Use the distributive property to multiply 4a^{2}-1 by 9a^{2}+3 and combine like terms.

$$36a^{4}+3a^{2}-3-36a^{4}-3a^{2}+2$$

Combine 36a^{4} and -36a^{4} to get 0.

$$3a^{2}-3-3a^{2}+2$$

Combine 3a^{2} and -3a^{2} to get 0.

$$-3+2$$

Add -3 and 2 to get -1.

$$-1$$

Factor

$$-1$$