Pre-Algebra Examples

$9 k^{2} - 30 (k m) + 25 m^{2}$

Step 1

Remove parentheses.

$9 k^{2} - 30 k m + 25 m^{2}$

Step 2

Factor using the perfect square rule.

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Step 2.1

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

${(3 k)}^{2} - 30 k m + 25 m^{2}$

Step 2.2

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

${(3 k)}^{2} - 30 k m + {(5 m)}^{2}$

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.

$30 k m = 2 \cdot (3 k) \cdot (5 m)$

Step 2.4

Rewrite the polynomial.

${(3 k)}^{2} - 2 \cdot (3 k) \cdot (5 m) + {(5 m)}^{2}$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 k$ and $b = 5 m$ .

${(3 k - 5 m)}^{2}$