125x3+343y3 can also be written (5x)3+(7y)3. It helps to rewrite the constants like this because there is a general factoring rule: a3+b3 = (a+b)(a2-ab+b2). In this example, the a is 5x and the b is 7y. Plug in and get (5x+7y)(25x2-35xy+49y2).
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