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\left(7x-10y\right)\left(7x+10y\right)
Rewrite 49x^{2}-100y^{2} as \left(7x\right)^{2}-\left(10y\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).