Algebra Examples

$(x^{2} + 4) (y^{2} + 9)$

Step 1

Multiply the constant in the polynomial $x^{2} + 4$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$(x^{2} - 4 i^{2}) (y^{2} + 9)$

Step 2

Multiply the constant in the polynomial $y^{2} + 9$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$(x^{2} - 4 i^{2}) (y^{2} - 9 i^{2})$

Step 3

Rewrite $4 i^{2}$ as ${(2 i)}^{2}$ .

$(x^{2} - {(2 i)}^{2}) (y^{2} - 9 i^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - i^{2} = (a + i) (a - i)$ where $a = x$ and $i = 2 i$ .

$(x + 2 i) (x - (2 i)) (y^{2} - 9 i^{2})$

Step 5

Multiply $2$ by $- 1$ .

$(x + 2 i) (x - 2 i) (y^{2} - 9 i^{2})$

Step 6

Rewrite $9 i^{2}$ as ${(3 i)}^{2}$ .

$(x + 2 i) (x - 2 i) (y^{2} - {(3 i)}^{2})$

Step 7

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - i^{2} = (a + i) (a - i)$ where $a = y$ and $i = 3 i$ .

$(x + 2 i) (x - 2 i) ((y + 3 i) (y - (3 i)))$

Step 8

Factor.

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Step 8.1

Multiply $3$ by $- 1$ .

$(x + 2 i) (x - 2 i) ((y + 3 i) (y - 3 i))$

Step 8.2

Remove unnecessary parentheses.

$(x + 2 i) (x - 2 i) (y + 3 i) (y - 3 i)$