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\left(14y^{2}-15z^{6}\right)\left(14y^{2}+15z^{6}\right)
Rewrite 196y^{4}-225z^{12} as \left(14y^{2}\right)^{2}-\left(15z^{6}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).