Factor 25a^2-0.01b^10

$25 a^{2} - 0.01 b^{10}$

Step 1

Factor $0.01$ out of $25 a^{2} - 0.01 b^{10}$ .

Factor $0.01$ out of $25 a^{2}$ .

$0.01 (2500 a^{2}) - 0.01 b^{10}$

Factor $0.01$ out of $- 0.01 b^{10}$ .

$0.01 (2500 a^{2}) + 0.01 (- b^{10})$

Factor $0.01$ out of $0.01 (2500 a^{2}) + 0.01 (- b^{10})$ .

$0.01 (2500 a^{2} - b^{10})$

Step 2

Rewrite $2500 a^{2}$ as ${(50 a)}^{2}$ .

$0.01 ({(50 a)}^{2} - b^{10})$

Step 3

Rewrite $b^{10}$ as ${(b^{5})}^{2}$ .

$0.01 ({(50 a)}^{2} - {(b^{5})}^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 50 a$ and $b = b^{5}$ .

$0.01 ((50 a + b^{5}) (50 a - b^{5}))$

Remove unnecessary parentheses.

$0.01 (50 a + b^{5}) (50 a - b^{5})$

Factor 25a^2-0.01b^10

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