Algebra Examples

$x^{3} + 10 x^{2} + 25 x$

Step 1

Factor $x$ out of $x^{3} + 10 x^{2} + 25 x$ .

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Step 1.1

Factor $x$ out of $x^{3}$ .

$x \cdot x^{2} + 10 x^{2} + 25 x$

Step 1.2

Factor $x$ out of $10 x^{2}$ .

$x \cdot x^{2} + x (10 x) + 25 x$

Step 1.3

Factor $x$ out of $25 x$ .

$x \cdot x^{2} + x (10 x) + x \cdot 25$

Step 1.4

Factor $x$ out of $x \cdot x^{2} + x (10 x)$ .

$x (x^{2} + 10 x) + x \cdot 25$

Step 1.5

Factor $x$ out of $x (x^{2} + 10 x) + x \cdot 25$ .

$x (x^{2} + 10 x + 25)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$x (x^{2} + 10 x + 5^{2})$

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.

$10 x = 2 \cdot x \cdot 5$

Step 2.3

Rewrite the polynomial.

$x (x^{2} + 2 \cdot x \cdot 5 + 5^{2})$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 5$ .

$x {(x + 5)}^{2}$