If (125x³ − 343y³) ÷ (5x − 7y) = Ax² − By² + Cxy, then find the value of (2A + B - C).
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Correct answer: A
Explanation
(125x³ − 343y³) ÷ (5x − 7y) = Ax² − By² + Cxy
a³ − b³ = (a − b)(a² + ab + b²)
125x³ − 343y³= (5x)³ − (7y)³= (5x − 7y)(25x² + 35xy + 49y²)
(125x³ − 343y³) ÷ (5x − 7y)= 25x² + 35xy + 49y²
Ax² − By² + Cxy = 25x² + 35xy + 49y²
A = 25
−B = 49 ⇒ B = −49
C = 35
2A + B − C= 2(25) + (−49) − 35
= 50 − 49 − 35
= −34