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Examples

(2 y + 3) (y + 2)

$(2 y + 3) (y + 2)$

Step 1

Expand

(2 y + 3) (y + 2)

$(2 y + 3) (y + 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

2 y (y + 2) + 3 (y + 2)

$2 y (y + 2) + 3 (y + 2)$

Step 1.2

Apply the distributive property.

2 y \cdot y + 2 y \cdot 2 + 3 (y + 2)

$2 y \cdot y + 2 y \cdot 2 + 3 (y + 2)$

Step 1.3

Apply the distributive property.

2 y \cdot y + 2 y \cdot 2 + 3 y + 3 \cdot 2

$2 y \cdot y + 2 y \cdot 2 + 3 y + 3 \cdot 2$

2 y \cdot y + 2 y \cdot 2 + 3 y + 3 \cdot 2

$2 y \cdot y + 2 y \cdot 2 + 3 y + 3 \cdot 2$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply

y

$y$ by

y

$y$ by adding the exponents.

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Step 2.1.1.1

Move

y

$y$ .

2 (y \cdot y) + 2 y \cdot 2 + 3 y + 3 \cdot 2

$2 (y \cdot y) + 2 y \cdot 2 + 3 y + 3 \cdot 2$

Step 2.1.1.2

Multiply

y

$y$ by

y

$y$ .

2 y^{2} + 2 y \cdot 2 + 3 y + 3 \cdot 2

$2 y^{2} + 2 y \cdot 2 + 3 y + 3 \cdot 2$

2 y^{2} + 2 y \cdot 2 + 3 y + 3 \cdot 2

$2 y^{2} + 2 y \cdot 2 + 3 y + 3 \cdot 2$

Step 2.1.2

Multiply

2

$2$ by

2

$2$ .

2 y^{2} + 4 y + 3 y + 3 \cdot 2

$2 y^{2} + 4 y + 3 y + 3 \cdot 2$

Step 2.1.3

Multiply

3

$3$ by

2

$2$ .

2 y^{2} + 4 y + 3 y + 6

$2 y^{2} + 4 y + 3 y + 6$

2 y^{2} + 4 y + 3 y + 6

$2 y^{2} + 4 y + 3 y + 6$

Step 2.2

Add

4 y

$4 y$ and

3 y

$3 y$ .

2 y^{2} + 7 y + 6

$2 y^{2} + 7 y + 6$

2 y^{2} + 7 y + 6

$2 y^{2} + 7 y + 6$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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