Solve (3x+2y)(x-1/3y)

$$( 3 x + 2 y ) ( x - \frac { 1 } { 3 } y )$$

Evaluate

$$xy-\frac{2y^{2}}{3}+3x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+2y by each term of x-\frac{1}{3}y.

$$3x^{2}+3x\left(-\frac{1}{3}\right)y+2yx+2y\left(-\frac{1}{3}\right)y$$

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

$$3x^{2}+3x\left(-\frac{1}{3}\right)y+2yx+2y^{2}\left(-\frac{1}{3}\right)$$

Cancel out 3 and 3.

$$3x^{2}-xy+2yx+2y^{2}\left(-\frac{1}{3}\right)$$

Combine -xy and 2yx to get xy.

$$3x^{2}+xy+2y^{2}\left(-\frac{1}{3}\right)$$

Express 2\left(-\frac{1}{3}\right) as a single fraction.

$$3x^{2}+xy+\frac{2\left(-1\right)}{3}y^{2}$$

Multiply 2 and -1 to get -2.

$$3x^{2}+xy+\frac{-2}{3}y^{2}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$3x^{2}+xy-\frac{2}{3}y^{2}$$

Expand

$$xy-\frac{2y^{2}}{3}+3x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+2y by each term of x-\frac{1}{3}y.

$$3x^{2}+3x\left(-\frac{1}{3}\right)y+2yx+2y\left(-\frac{1}{3}\right)y$$

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

$$3x^{2}+3x\left(-\frac{1}{3}\right)y+2yx+2y^{2}\left(-\frac{1}{3}\right)$$

Cancel out 3 and 3.

$$3x^{2}-xy+2yx+2y^{2}\left(-\frac{1}{3}\right)$$

Combine -xy and 2yx to get xy.

$$3x^{2}+xy+2y^{2}\left(-\frac{1}{3}\right)$$

Express 2\left(-\frac{1}{3}\right) as a single fraction.

$$3x^{2}+xy+\frac{2\left(-1\right)}{3}y^{2}$$

Multiply 2 and -1 to get -2.

$$3x^{2}+xy+\frac{-2}{3}y^{2}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$3x^{2}+xy-\frac{2}{3}y^{2}$$