Solve -2x(1/3x-1/5y+1)

$$- 2 x ( \frac { 1 } { 3 } x - \frac { 1 } { 5 } y + 1 )$$

Evaluate

$$-\frac{2x\left(5x-3y+15\right)}{15}$$

Solution Steps

Use the distributive property to multiply -2x by \frac{1}{3}x-\frac{1}{5}y+1.

$$-2x\times \frac{1}{3}x-2x\left(-\frac{1}{5}\right)y-2x$$

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

$$-2x^{2}\times \frac{1}{3}-2x\left(-\frac{1}{5}\right)y-2x$$

Multiply -2 and \frac{1}{3} to get \frac{-2}{3}.

$$\frac{-2}{3}x^{2}-2x\left(-\frac{1}{5}\right)y-2x$$

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

$$-\frac{2}{3}x^{2}-2x\left(-\frac{1}{5}\right)y-2x$$

Express -2\left(-\frac{1}{5}\right) as a single fraction.

$$-\frac{2}{3}x^{2}+\frac{-2\left(-1\right)}{5}xy-2x$$

Multiply -2 and -1 to get 2.

$$-\frac{2}{3}x^{2}+\frac{2}{5}xy-2x$$

Expand

$$\frac{2xy}{5}-\frac{2x^{2}}{3}-2x$$

Solution Steps

Use the distributive property to multiply -2x by \frac{1}{3}x-\frac{1}{5}y+1.

$$-2x\times \frac{1}{3}x-2x\left(-\frac{1}{5}\right)y-2x$$

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

$$-2x^{2}\times \frac{1}{3}-2x\left(-\frac{1}{5}\right)y-2x$$

Multiply -2 and \frac{1}{3} to get \frac{-2}{3}.

$$\frac{-2}{3}x^{2}-2x\left(-\frac{1}{5}\right)y-2x$$

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

$$-\frac{2}{3}x^{2}-2x\left(-\frac{1}{5}\right)y-2x$$

Express -2\left(-\frac{1}{5}\right) as a single fraction.

$$-\frac{2}{3}x^{2}+\frac{-2\left(-1\right)}{5}xy-2x$$

Multiply -2 and -1 to get 2.

$$-\frac{2}{3}x^{2}+\frac{2}{5}xy-2x$$