Solve 2/3a(6a+1)(6a-1)-0,5a(12a^2+2/3)

$$\frac { 2 } { 3 } a ( 6 a + 1 ) ( 6 a - 1 ) - 0,5 a ( 12 a ^ { 2 } + \frac { 2 } { 3 } )$$

Evaluate

$$a\left(18a^{2}-1\right)$$

Solution Steps

Use the distributive property to multiply \frac{2}{3}a by 6a+1.

$$\left(4a^{2}+\frac{2}{3}a\right)\left(6a-1\right)-0,5a\left(12a^{2}+\frac{2}{3}\right)$$

Use the distributive property to multiply 4a^{2}+\frac{2}{3}a by 6a-1 and combine like terms.

$$24a^{3}-\frac{2}{3}a-0,5a\left(12a^{2}+\frac{2}{3}\right)$$

Use the distributive property to multiply -0,5a by 12a^{2}+\frac{2}{3}.

$$24a^{3}-\frac{2}{3}a-6a^{3}-\frac{1}{3}a$$

Combine 24a^{3} and -6a^{3} to get 18a^{3}.

$$18a^{3}-\frac{2}{3}a-\frac{1}{3}a$$

Combine -\frac{2}{3}a and -\frac{1}{3}a to get -a.

$$18a^{3}-a$$

Expand

$$18a^{3}-a$$

Solution Steps

Use the distributive property to multiply \frac{2}{3}a by 6a+1.

$$\left(4a^{2}+\frac{2}{3}a\right)\left(6a-1\right)-0,5a\left(12a^{2}+\frac{2}{3}\right)$$

Use the distributive property to multiply 4a^{2}+\frac{2}{3}a by 6a-1 and combine like terms.

$$24a^{3}-\frac{2}{3}a-0,5a\left(12a^{2}+\frac{2}{3}\right)$$

Use the distributive property to multiply -0,5a by 12a^{2}+\frac{2}{3}.

$$24a^{3}-\frac{2}{3}a-6a^{3}-\frac{1}{3}a$$

Combine 24a^{3} and -6a^{3} to get 18a^{3}.

$$18a^{3}-\frac{2}{3}a-\frac{1}{3}a$$

Combine -\frac{2}{3}a and -\frac{1}{3}a to get -a.

$$18a^{3}-a$$