Algebra Examples

$(2 + 3 d) (2 + 3 d)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(2 + 3 d) (2 + 3 d)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 (2 + 3 d) + 3 d (2 + 3 d)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $2$ .

$4 + 2 (3 d) + 3 d \cdot 2 + 3 d (3 d)$

Step 3.1.2

Multiply $3$ by $2$ .

$4 + 6 d + 3 d \cdot 2 + 3 d (3 d)$

Step 3.1.3

Multiply $2$ by $3$ .

$4 + 6 d + 6 d + 3 d (3 d)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$4 + 6 d + 6 d + 3 \cdot 3 d \cdot d$

Step 3.1.5

Multiply $d$ by $d$ by adding the exponents.

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Step 3.1.5.1

Move $d$ .

$4 + 6 d + 6 d + 3 \cdot 3 (d \cdot d)$

Step 3.1.5.2

Multiply $d$ by $d$ .

$4 + 6 d + 6 d + 3 \cdot 3 d^{2}$

Step 3.1.6

Multiply $3$ by $3$ .

$4 + 6 d + 6 d + 9 d^{2}$

Step 3.2

Add $6 d$ and $6 d$ .

$4 + 12 d + 9 d^{2}$

Step 4

Move $4$ .

$12 d + 9 d^{2} + 4$

Step 5

Reorder $12 d$ and $9 d^{2}$ .

$9 d^{2} + 12 d + 4$