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\left(5p-6q\right)\left(5p+6q\right)
Rewrite 25p^{2}-36q^{2} as \left(5p\right)^{2}-\left(6q\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).