Precalculus Examples

$4 {(a + 1)}^{2} - 6 (a + 1) + 8$

Step 1

Factor $2$ out of $4 {(a + 1)}^{2} - 6 (a + 1) + 8$ .

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Step 1.1

Factor $2$ out of $4 {(a + 1)}^{2}$ .

$2 (2 {(a + 1)}^{2}) - 6 (a + 1) + 8$

Step 1.2

Factor $2$ out of $- 6 (a + 1)$ .

$2 (2 {(a + 1)}^{2}) + 2 (- 3 (a + 1)) + 8$

Step 1.3

Factor $2$ out of $8$ .

$2 (2 {(a + 1)}^{2}) + 2 (- 3 (a + 1)) + 2 (4)$

Step 1.4

Factor $2$ out of $2 (2 {(a + 1)}^{2}) + 2 (- 3 (a + 1))$ .

$2 (2 {(a + 1)}^{2} - 3 (a + 1)) + 2 (4)$

Step 1.5

Factor $2$ out of $2 (2 {(a + 1)}^{2} - 3 (a + 1)) + 2 (4)$ .

$2 (2 {(a + 1)}^{2} - 3 (a + 1) + 4)$

Step 2

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

$2 (2 ((a + 1) (a + 1)) - 3 (a + 1) + 4)$

Step 3

Expand $(a + 1) (a + 1)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$2 (2 (a (a + 1) + 1 (a + 1)) - 3 (a + 1) + 4)$

Step 3.2

Apply the distributive property.

$2 (2 (a \cdot a + a \cdot 1 + 1 (a + 1)) - 3 (a + 1) + 4)$

Step 3.3

Apply the distributive property.

$2 (2 (a \cdot a + a \cdot 1 + 1 a + 1 \cdot 1) - 3 (a + 1) + 4)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $a$ by $a$ .

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

Step 4.1.2

Multiply $a$ by $1$ .

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

Step 4.1.3

Multiply $a$ by $1$ .

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

Step 4.1.4

Multiply $1$ by $1$ .

$2 (2 (a^{2} + a + a + 1) - 3 (a + 1) + 4)$

Step 4.2

Add $a$ and $a$ .

$2 (2 (a^{2} + 2 a + 1) - 3 (a + 1) + 4)$

Step 5

Apply the distributive property.

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

Step 6

Simplify.

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Step 6.1

Multiply $2$ by $2$ .

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

Step 6.2

Multiply $2$ by $1$ .

$2 (2 a^{2} + 4 a + 2 - 3 (a + 1) + 4)$

Step 7

Apply the distributive property.

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

Step 8

Multiply $- 3$ by $1$ .

$2 (2 a^{2} + 4 a + 2 - 3 a - 3 + 4)$

Step 9

Subtract $3 a$ from $4 a$ .

$2 (2 a^{2} + a + 2 - 3 + 4)$

Step 10

Subtract $3$ from $2$ .

$2 (2 a^{2} + a - 1 + 4)$

Step 11

Add $- 1$ and $4$ .

$2 (2 a^{2} + a + 3)$