Korzystamy ze wzoru na różnicę kwadratów:

$a^2-b^2=\left(a+b\right)\left(a-b\right)$  

$\text{a)}4a^2-1={\left(2a\right)}^2-1^2=\left(2a+1\right)\left(2a-1\right)$  

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$\text{b)}25-49x^2=5^2-{\left(7x\right)}^2=\left(5+7x\right)\left(5-7x\right)$  

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$\text{c)}9m^2-n^2={\left(3m\right)}^2-n^2=\left(3m+n\right)\left(3m-n\right)$  

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$\text{d)}{x}^2{y}^2-16={\left(xy\right)}^2-4^2=\left(xy+4\right)\left(xy-4\right)$  

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$\text{e)}\frac{25}{16}{p}^4-1={\left(\frac{5}{4}{p}^2\right)}^2-1^2=\left(\frac{5}{4}{p}^2+1\right)\left(\frac{5}{4}{p}^2-1\right)$  

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$\text{f)}2a^2-4b^2={\left(\sqrt{2}a\right)}^2-{\left(2b\right)}^2=\left(\sqrt{2}a+2b\right)\left(\sqrt{2}a-2b\right)$