Solve (1+2/3)^2+(-6a^2-2a)*(a+2/3)*(a-2/3)

$$( 1 + \frac { 2 } { 3 } ) ^ { 2 } + ( - 6 a ^ { 2 } - 2 a ) \cdot ( a + \frac { 2 } { 3 } ) \cdot ( a - \frac { 2 } { 3 } )$$

Evaluate

$$-6a^{4}-2a^{3}+\frac{8a^{2}}{3}+\frac{8a}{9}+\frac{25}{9}$$

Solution Steps

Add 1 and \frac{2}{3} to get \frac{5}{3}.

$$\left(\frac{5}{3}\right)^{2}+\left(-6a^{2}-2a\right)\left(a+\frac{2}{3}\right)\left(a-\frac{2}{3}\right)$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{25}{9}+\left(-6a^{2}-2a\right)\left(a+\frac{2}{3}\right)\left(a-\frac{2}{3}\right)$$

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

$$\frac{25}{9}+\left(-6a^{3}-6a^{2}-\frac{4}{3}a\right)\left(a-\frac{2}{3}\right)$$

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

$$\frac{25}{9}-6a^{4}-2a^{3}+\frac{8}{3}a^{2}+\frac{8}{9}a$$

Expand

$$-6a^{4}-2a^{3}+\frac{8a^{2}}{3}+\frac{8a}{9}+\frac{25}{9}$$

Solution Steps

Add 1 and \frac{2}{3} to get \frac{5}{3}.

$$\left(\frac{5}{3}\right)^{2}+\left(-6a^{2}-2a\right)\left(a+\frac{2}{3}\right)\left(a-\frac{2}{3}\right)$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{25}{9}+\left(-6a^{2}-2a\right)\left(a+\frac{2}{3}\right)\left(a-\frac{2}{3}\right)$$

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

$$\frac{25}{9}+\left(-6a^{3}-6a^{2}-\frac{4}{3}a\right)\left(a-\frac{2}{3}\right)$$

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

$$\frac{25}{9}-6a^{4}-2a^{3}+\frac{8}{3}a^{2}+\frac{8}{9}a$$