Algebra Examples

3 + 6 b + 3 b^{2}

$3 + 6 b + 3 b^{2}$

Step 1

Factor

3

$3$ out of

3 + 6 b + 3 b^{2}

$3 + 6 b + 3 b^{2}$ .

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Step 1.1

Factor

3

$3$ out of

3

$3$ .

3 \cdot 1 + 6 b + 3 b^{2}

$3 \cdot 1 + 6 b + 3 b^{2}$

Step 1.2

Factor

3

$3$ out of

6 b

$6 b$ .

3 \cdot 1 + 3 (2 b) + 3 b^{2}

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

Step 1.3

Factor

3

$3$ out of

3 \cdot 1 + 3 (2 b)

$3 \cdot 1 + 3 (2 b)$ .

3 \cdot (1 + 2 b) + 3 b^{2}

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

Step 1.4

Factor

3

$3$ out of

3 \cdot (1 + 2 b) + 3 b^{2}

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

3 (1 + 2 b + b^{2})

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

3 (1 + 2 b + b^{2})

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

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

3 (1^{2} + 2 b + b^{2})

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

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

2 b = 2 \cdot 1 \cdot b

$2 b = 2 \cdot 1 \cdot b$

Step 2.3

Rewrite the polynomial.

3 (1^{2} + 2 \cdot 1 \cdot b + b^{2})

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

Step 2.4

Factor using the perfect square trinomial rule

a^{2} + 2 a b + b^{2} = {(a + b)}^{2}

$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where

a = 1

$a = 1$ and

b = b

$b = b$ .

3 {(1 + b)}^{2}

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

3 {(1 + b)}^{2}

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

3 + 6 b + 3 b^{2}

$3 + 6 b + 3 b^{2}$

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