Algebra Examples

$25 y^{2} x^{2} + 60 y x^{2} + 36 x^{2}$

Step 1

Factor $x^{2}$ out of $25 y^{2} x^{2} + 60 y x^{2} + 36 x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $25 y^{2} x^{2}$ .

$x^{2} (25 y^{2}) + 60 y x^{2} + 36 x^{2}$

Step 1.2

Factor $x^{2}$ out of $60 y x^{2}$ .

$x^{2} (25 y^{2}) + x^{2} (60 y) + 36 x^{2}$

Step 1.3

Factor $x^{2}$ out of $36 x^{2}$ .

$x^{2} (25 y^{2}) + x^{2} (60 y) + x^{2} \cdot 36$

Step 1.4

Factor $x^{2}$ out of $x^{2} (25 y^{2}) + x^{2} (60 y)$ .

$x^{2} (25 y^{2} + 60 y) + x^{2} \cdot 36$

Step 1.5

Factor $x^{2}$ out of $x^{2} (25 y^{2} + 60 y) + x^{2} \cdot 36$ .

$x^{2} (25 y^{2} + 60 y + 36)$

Step 2

Factor using the perfect square rule.

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Step 2.1

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

$x^{2} ({(5 y)}^{2} + 60 y + 36)$

Step 2.2

Rewrite $36$ as $6^{2}$ .

$x^{2} ({(5 y)}^{2} + 60 y + 6^{2})$

Step 2.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$60 y = 2 \cdot (5 y) \cdot 6$

Step 2.4

Rewrite the polynomial.

$x^{2} ({(5 y)}^{2} + 2 \cdot (5 y) \cdot 6 + 6^{2})$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5 y$ and $b = 6$ .

$x^{2} {(5 y + 6)}^{2}$