Pre-Algebra Examples

${(1 + x y)}^{2}$

Step 1

Rewrite ${(1 + x y)}^{2}$ as $(1 + x y) (1 + x y)$ .

$(1 + x y) (1 + x y)$

Step 2

Expand $(1 + x y) (1 + x y)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$1 (1 + x y) + x y (1 + x y)$

Step 2.2

Apply the distributive property.

$1 \cdot 1 + 1 (x y) + x y (1 + x y)$

Step 2.3

Apply the distributive property.

$1 \cdot 1 + 1 (x y) + x y \cdot 1 + x y (x y)$

$1 \cdot 1 + 1 (x y) + x y \cdot 1 + x y (x y)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $1$ by $1$ .

$1 + 1 (x y) + x y \cdot 1 + x y (x y)$

Step 3.1.2

Multiply $x y$ by $1$ .

$1 + x y + x y \cdot 1 + x y (x y)$

Step 3.1.3

Multiply $x$ by $1$ .

$1 + x y + x y + x y (x y)$

Step 3.1.4

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 3.1.4.1

Move $x$ .

$1 + x y + x y + x \cdot x y \cdot y$

Step 3.1.4.2

Multiply $x$ by $x$ .

$1 + x y + x y + x^{2} y \cdot y$

$1 + x y + x y + x^{2} y \cdot y$

Step 3.1.5

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 3.1.5.1

Move $y$ .

$1 + x y + x y + x^{2} (y \cdot y)$

Step 3.1.5.2

Multiply $y$ by $y$ .

$1 + x y + x y + x^{2} y^{2}$

$1 + x y + x y + x^{2} y^{2}$

$1 + x y + x y + x^{2} y^{2}$

Step 3.2

Add $x y$ and $x y$ .

$1 + 2 x y + x^{2} y^{2}$

$1 + 2 x y + x^{2} y^{2}$

Step 4

Move $1$ .

$2 x y + x^{2} y^{2} + 1$

Step 5

Reorder $2 x y$ and $x^{2} y^{2}$ .

$x^{2} y^{2} + 2 x y + 1$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$