Basic Math Examples

$a b^{2} + b^{2} + a^{2} - 2 a - 3$

Step 1

Regroup terms.

$a b^{2} + b^{2} + a^{2} - 2 a - 3$

Step 2

Factor $b^{2}$ out of $a b^{2} + b^{2}$ .

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Step 2.1

Factor $b^{2}$ out of $a b^{2}$ .

$b^{2} a + b^{2} + a^{2} - 2 a - 3$

Step 2.2

Multiply by $1$ .

$b^{2} a + b^{2} \cdot 1 + a^{2} - 2 a - 3$

Step 2.3

Factor $b^{2}$ out of $b^{2} a + b^{2} \cdot 1$ .

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

Step 3

Factor $a^{2} - 2 a - 3$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Step 3.2

Write the factored form using these integers.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Factor $a + 1$ out of $(a - 3) (a + 1)$ .

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

Step 4.3

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

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