Answer:
7(4x^2 + 7y^2)(2x - 3y)(6x - 7y)
Step-by-step explanation:
To factorize the expression 8x^3 - 84x^2y + 294xy^2 - 343y^3, we can look for a common factor among the terms. In this case, the common factor is 7, so we can rewrite the expression as:
8x^3 - 84x^2y + 294xy^2 - 343y^3
= 7(8x^3 - 12x^2y + 42xy^2 - 49y^3)
Next, we can factorize the expression within the parentheses by grouping:
= 7(8x^3 - 12x^2y + 42xy^2 - 49y^3)
= 7[4x^2(2x - 3y) + 7y^2(6x - 7y)]
Therefore, the factored form of the expression 8x^3 - 84x^2y + 294xy^2 - 343y^3 is 7(4x^2 + 7y^2)(2x - 3y)(6x - 7y).
