Solve (-1/7a-3y)(3y-1/7a)

$$( - \frac { 1 } { 7 } a - 3 y ) ( 3 y - \frac { 1 } { 7 } a )$$

Evaluate

$$\frac{a^{2}}{49}-9y^{2}$$

Solution Steps

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

$$\left(-\frac{1}{7}a\right)^{2}-\left(3y\right)^{2}$$

Expand \left(-\frac{1}{7}a\right)^{2}.

$$\left(-\frac{1}{7}\right)^{2}a^{2}-\left(3y\right)^{2}$$

Calculate -\frac{1}{7} to the power of 2 and get \frac{1}{49}.

$$\frac{1}{49}a^{2}-\left(3y\right)^{2}$$

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

$$\frac{1}{49}a^{2}-3^{2}y^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{49}a^{2}-9y^{2}$$

Expand

$$\frac{a^{2}}{49}-9y^{2}$$

Solution Steps

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

$$\left(-\frac{1}{7}a\right)^{2}-\left(3y\right)^{2}$$

Expand \left(-\frac{1}{7}a\right)^{2}.

$$\left(-\frac{1}{7}\right)^{2}a^{2}-\left(3y\right)^{2}$$

Calculate -\frac{1}{7} to the power of 2 and get \frac{1}{49}.

$$\frac{1}{49}a^{2}-\left(3y\right)^{2}$$

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

$$\frac{1}{49}a^{2}-3^{2}y^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{1}{49}a^{2}-9y^{2}$$