Solve 5(x-3y)(1/5x+3/5y)

$$5 ( x - 3 y ) ( \frac { 1 } { 5 } x + \frac { 3 } { 5 } y )$$

Evaluate

$$x^{2}-9y^{2}$$

Solution Steps

Use the distributive property to multiply 5 by x-3y.

$$\left(5x-15y\right)\left(\frac{1}{5}x+\frac{3}{5}y\right)$$

Apply the distributive property by multiplying each term of 5x-15y by each term of \frac{1}{5}x+\frac{3}{5}y.

$$5x\times \frac{1}{5}x+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y\times \frac{3}{5}y$$

Multiply x and x to get x^{2}.

$$5x^{2}\times \frac{1}{5}+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y\times \frac{3}{5}y$$

Multiply y and y to get y^{2}.

$$5x^{2}\times \frac{1}{5}+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y^{2}\times \frac{3}{5}$$

Cancel out 5 and 5.

$$x^{2}+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y^{2}\times \frac{3}{5}$$

Cancel out 5 and 5.

$$x^{2}+3xy-15y\times \frac{1}{5}x-15y^{2}\times \frac{3}{5}$$

Multiply -15 and \frac{1}{5} to get \frac{-15}{5}.

$$x^{2}+3xy+\frac{-15}{5}yx-15y^{2}\times \frac{3}{5}$$

Divide -15 by 5 to get -3.

$$x^{2}+3xy-3yx-15y^{2}\times \frac{3}{5}$$

Combine 3xy and -3yx to get 0.

$$x^{2}-15y^{2}\times \frac{3}{5}$$

Express -15\times \frac{3}{5} as a single fraction.

$$x^{2}+\frac{-15\times 3}{5}y^{2}$$

Multiply -15 and 3 to get -45.

$$x^{2}+\frac{-45}{5}y^{2}$$

Divide -45 by 5 to get -9.

$$x^{2}-9y^{2}$$

Expand

$$x^{2}-9y^{2}$$

Solution Steps

Use the distributive property to multiply 5 by x-3y.

$$\left(5x-15y\right)\left(\frac{1}{5}x+\frac{3}{5}y\right)$$

Apply the distributive property by multiplying each term of 5x-15y by each term of \frac{1}{5}x+\frac{3}{5}y.

$$5x\times \frac{1}{5}x+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y\times \frac{3}{5}y$$

Multiply x and x to get x^{2}.

$$5x^{2}\times \frac{1}{5}+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y\times \frac{3}{5}y$$

Multiply y and y to get y^{2}.

$$5x^{2}\times \frac{1}{5}+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y^{2}\times \frac{3}{5}$$

Cancel out 5 and 5.

$$x^{2}+5x\times \frac{3}{5}y-15y\times \frac{1}{5}x-15y^{2}\times \frac{3}{5}$$

Cancel out 5 and 5.

$$x^{2}+3xy-15y\times \frac{1}{5}x-15y^{2}\times \frac{3}{5}$$

Multiply -15 and \frac{1}{5} to get \frac{-15}{5}.

$$x^{2}+3xy+\frac{-15}{5}yx-15y^{2}\times \frac{3}{5}$$

Divide -15 by 5 to get -3.

$$x^{2}+3xy-3yx-15y^{2}\times \frac{3}{5}$$

Combine 3xy and -3yx to get 0.

$$x^{2}-15y^{2}\times \frac{3}{5}$$

Express -15\times \frac{3}{5} as a single fraction.

$$x^{2}+\frac{-15\times 3}{5}y^{2}$$

Multiply -15 and 3 to get -45.

$$x^{2}+\frac{-45}{5}y^{2}$$

Divide -45 by 5 to get -9.

$$x^{2}-9y^{2}$$