Solve (1/3+3p)(1/3-3p):quadr)(2y

$$( \frac { 1 } { 3 } + 3 p ) ( \frac { 1 } { 3 } - 3 p ) : \quad r ) ( 2 y$$

Evaluate

$$\frac{1-81p^{2}}{9r}$$

Short Solution Steps

Consider \left(\frac{1}{3}+3p\right)\left(\frac{1}{3}-3p\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\frac{1}{3}\right)^{2}-\left(3p\right)^{2}}{r}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}-\left(3p\right)^{2}}{r}$$

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

$$\frac{\frac{1}{9}-3^{2}p^{2}}{r}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{1}{9}-9p^{2}}{r}$$

Expand

$$-\frac{81p^{2}-1}{9r}$$

Short Solution Steps

Consider \left(\frac{1}{3}+3p\right)\left(\frac{1}{3}-3p\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\frac{1}{3}\right)^{2}-\left(3p\right)^{2}}{r}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}-\left(3p\right)^{2}}{r}$$

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

$$\frac{\frac{1}{9}-3^{2}p^{2}}{r}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{1}{9}-9p^{2}}{r}$$