Algebra Examples

$\frac{1}{2} x y^{2} + 3 x - \frac{5}{2} x y^{2} + \frac{3}{7} x^{2} - 4 x$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Multiply $\frac{1}{2} (x y^{2})$ .

Tap for more steps...

Step 1.1.1

Combine $x$ and $\frac{1}{2}$ .

$\frac{x}{2} y^{2} + 3 x - \frac{5}{2} \cdot (x y^{2}) + \frac{3}{7} x^{2} - 4 x$

Step 1.1.2

Combine $\frac{x}{2}$ and $y^{2}$ .

$\frac{x y^{2}}{2} + 3 x - \frac{5}{2} \cdot (x y^{2}) + \frac{3}{7} x^{2} - 4 x$

Step 1.2

Multiply $- \frac{5}{2} (x y^{2})$ .

Tap for more steps...

Step 1.2.1

Combine $x$ and $\frac{5}{2}$ .

$\frac{x y^{2}}{2} + 3 x - \frac{x \cdot 5}{2} y^{2} + \frac{3}{7} x^{2} - 4 x$

Step 1.2.2

Combine $y^{2}$ and $\frac{x \cdot 5}{2}$ .

$\frac{x y^{2}}{2} + 3 x - \frac{y^{2} (x \cdot 5)}{2} + \frac{3}{7} x^{2} - 4 x$

Step 1.3

Move $5$ to the left of $y^{2} x$ .

$\frac{x y^{2}}{2} + 3 x - \frac{5 \cdot (y^{2} x)}{2} + \frac{3}{7} x^{2} - 4 x$

Step 1.4

Combine $\frac{3}{7}$ and $x^{2}$ .

$\frac{x y^{2}}{2} + 3 x - \frac{5 y^{2} x}{2} + \frac{3 x^{2}}{7} - 4 x$

Step 2

Combine the numerators over the common denominator.

$3 x - 4 x + \frac{x y^{2} - 5 y^{2} x}{2} + \frac{3 x^{2}}{7}$

Step 3

Subtract $5 y^{2} x$ from $x y^{2}$ .

Tap for more steps...

Step 3.1

Move $y^{2}$ .

$3 x - 4 x + \frac{x y^{2} - 5 x y^{2}}{2} + \frac{3 x^{2}}{7}$

Step 3.2

Subtract $5 x y^{2}$ from $x y^{2}$ .

$3 x - 4 x + \frac{- 4 x y^{2}}{2} + \frac{3 x^{2}}{7}$

Step 4

Cancel the common factor of $- 4$ and $2$ .

Tap for more steps...

Step 4.1

Factor $2$ out of $- 4 x y^{2}$ .

$3 x - 4 x + \frac{2 (- 2 x y^{2})}{2} + \frac{3 x^{2}}{7}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $2$ out of $2$ .

$3 x - 4 x + \frac{2 (- 2 x y^{2})}{2 (1)} + \frac{3 x^{2}}{7}$

Step 4.2.2

Cancel the common factor.

$3 x - 4 x + \frac{2 (- 2 x y^{2})}{2 \cdot 1} + \frac{3 x^{2}}{7}$

Step 4.2.3

Rewrite the expression.

$3 x - 4 x + \frac{- 2 x y^{2}}{1} + \frac{3 x^{2}}{7}$

Step 4.2.4

Divide $- 2 x y^{2}$ by $1$ .

$3 x - 4 x - 2 x y^{2} + \frac{3 x^{2}}{7}$

Step 5

Subtract $4 x$ from $3 x$ .

$- x - 2 x y^{2} + \frac{3 x^{2}}{7}$