Algebra Examples

$\frac{7}{4} x y + \frac{7}{3} y^{3} + y^{3} - \frac{11}{4} x y$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{7}{4} (x y)$ .

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Step 1.1.1

Combine $x$ and $\frac{7}{4}$ .

$\frac{x \cdot 7}{4} y + \frac{7}{3} y^{3} + y^{3} - \frac{11}{4} \cdot (x y)$

Step 1.1.2

Combine $\frac{x \cdot 7}{4}$ and $y$ .

$\frac{x \cdot 7 y}{4} + \frac{7}{3} y^{3} + y^{3} - \frac{11}{4} \cdot (x y)$

Step 1.2

Move $7$ to the left of $x$ .

$\frac{7 \cdot x y}{4} + \frac{7}{3} y^{3} + y^{3} - \frac{11}{4} \cdot (x y)$

Step 1.3

Combine $\frac{7}{3}$ and $y^{3}$ .

$\frac{7 x y}{4} + \frac{7 y^{3}}{3} + y^{3} - \frac{11}{4} \cdot (x y)$

Step 1.4

Multiply $- \frac{11}{4} (x y)$ .

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Step 1.4.1

Combine $x$ and $\frac{11}{4}$ .

$\frac{7 x y}{4} + \frac{7 y^{3}}{3} + y^{3} - \frac{x \cdot 11}{4} y$

Step 1.4.2

Combine $y$ and $\frac{x \cdot 11}{4}$ .

$\frac{7 x y}{4} + \frac{7 y^{3}}{3} + y^{3} - \frac{y (x \cdot 11)}{4}$

Step 1.5

Move $11$ to the left of $y x$ .

$\frac{7 x y}{4} + \frac{7 y^{3}}{3} + y^{3} - \frac{11 y x}{4}$

Step 2

Combine the numerators over the common denominator.

$y^{3} + \frac{7 x y - 11 y x}{4} + \frac{7 y^{3}}{3}$

Step 3

Subtract $11 y x$ from $7 x y$ .

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Step 3.1

Move $y$ .

$y^{3} + \frac{7 x y - 11 x y}{4} + \frac{7 y^{3}}{3}$

Step 3.2

Subtract $11 x y$ from $7 x y$ .

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

Step 4

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

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Step 4.1

Factor $4$ out of $- 4 x y$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $4$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.2.4

Divide $- x y$ by $1$ .

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

Step 5

To write $y^{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 6

Combine $y^{3}$ and $\frac{3}{3}$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Add $y^{3} \cdot 3$ and $7 y^{3}$ .

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Step 8.1

Reorder $y^{3}$ and $3$ .

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

Step 8.2

Add $3 \cdot y^{3}$ and $7 y^{3}$ .

$- x y + \frac{10 \cdot y^{3}}{3}$

$- x y + \frac{10 y^{3}}{3}$