Basic Math Examples

$k (2 k + 1) (2 k + 3) + (2 k + 1)$

Step 1

Remove parentheses.

$k (2 k + 1) (2 k + 3) + 2 k + 1$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$(k (2 k) + k \cdot 1) (2 k + 3) + 2 k + 1$

Step 2.2

Rewrite using the commutative property of multiplication.

$(2 k \cdot k + k \cdot 1) (2 k + 3) + 2 k + 1$

Step 2.3

Multiply $k$ by $1$ .

$(2 k \cdot k + k) (2 k + 3) + 2 k + 1$

Step 2.4

Multiply $k$ by $k$ by adding the exponents.

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Step 2.4.1

Move $k$ .

$(2 (k \cdot k) + k) (2 k + 3) + 2 k + 1$

Step 2.4.2

Multiply $k$ by $k$ .

$(2 k^{2} + k) (2 k + 3) + 2 k + 1$

Step 2.5

Expand $(2 k^{2} + k) (2 k + 3)$ using the FOIL Method.

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Step 2.5.1

Apply the distributive property.

$2 k^{2} (2 k + 3) + k (2 k + 3) + 2 k + 1$

Step 2.5.2

Apply the distributive property.

$2 k^{2} (2 k) + 2 k^{2} \cdot 3 + k (2 k + 3) + 2 k + 1$

Step 2.5.3

Apply the distributive property.

$2 k^{2} (2 k) + 2 k^{2} \cdot 3 + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6

Simplify and combine like terms.

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Step 2.6.1

Simplify each term.

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Step 2.6.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 k^{2} k + 2 k^{2} \cdot 3 + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.2

Multiply $k^{2}$ by $k$ by adding the exponents.

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Step 2.6.1.2.1

Move $k$ .

$2 \cdot 2 (k \cdot k^{2}) + 2 k^{2} \cdot 3 + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.2.2

Multiply $k$ by $k^{2}$ .

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Step 2.6.1.2.2.1

Raise $k$ to the power of $1$ .

$2 \cdot 2 (k^{1} k^{2}) + 2 k^{2} \cdot 3 + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 2 k^{1 + 2} + 2 k^{2} \cdot 3 + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.2.3

Add $1$ and $2$ .

$2 \cdot 2 k^{3} + 2 k^{2} \cdot 3 + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.3

Multiply $2$ by $2$ .

$4 k^{3} + 2 k^{2} \cdot 3 + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.4

Multiply $3$ by $2$ .

$4 k^{3} + 6 k^{2} + k (2 k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.5

Rewrite using the commutative property of multiplication.

$4 k^{3} + 6 k^{2} + 2 k \cdot k + k \cdot 3 + 2 k + 1$

Step 2.6.1.6

Multiply $k$ by $k$ by adding the exponents.

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Step 2.6.1.6.1

Move $k$ .

$4 k^{3} + 6 k^{2} + 2 (k \cdot k) + k \cdot 3 + 2 k + 1$

Step 2.6.1.6.2

Multiply $k$ by $k$ .

$4 k^{3} + 6 k^{2} + 2 k^{2} + k \cdot 3 + 2 k + 1$

Step 2.6.1.7

Move $3$ to the left of $k$ .

$4 k^{3} + 6 k^{2} + 2 k^{2} + 3 k + 2 k + 1$

Step 2.6.2

Add $6 k^{2}$ and $2 k^{2}$ .

$4 k^{3} + 8 k^{2} + 3 k + 2 k + 1$

Step 3

Add $3 k$ and $2 k$ .

$4 k^{3} + 8 k^{2} + 5 k + 1$