Factor over the Complex Numbers 25x^2+144

$25 x^{2} + 144$

Step 1

Multiply the constant in the polynomial $25 x^{2} + 144$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$25 x^{2} - 144 i^{2}$

Step 2

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

${(5 x)}^{2} - 144 i^{2}$

Step 3

Rewrite $144 i^{2}$ as ${(12 i)}^{2}$ .

${(5 x)}^{2} - {(12 i)}^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - i^{2} = (a + i) (a - i)$ where $a = 5 x$ and $i = 12 i$ .

$(5 x + 12 i) (5 x - (12 i))$

Step 5

Multiply $12$ by $- 1$ .

$(5 x + 12 i) (5 x - 12 i)$

Factor over the Complex Numbers 25x^2+144

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