Algebra Examples

$4 x^{2} + 25$

Multiply the constant in the polynomial $4 x^{2} + 25$ by $- i^{2}$ where $i^{2}$ is equal to $- 1$ .

$4 x^{2} - 25 i^{2}$

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

${(2 x)}^{2} - 25 i^{2}$

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

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

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

$(2 x + 5 i) (2 x - (5 i))$

Multiply $5$ by $- 1$ .

$(2 x + 5 i) (2 x - 5 i)$