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If (8x3 - 27y3) ÷ (2x - 3y) = (Ax2 + Bxy + Cy2), then the value of (2A + B - C) is:
Answer & Solution
Correct Answer:
Option
C
$$\eqalign{
& \left( {8{x^3} - 27{y^3}} \right) \div \left( {2x - 3y} \right) = A{x^2} + Bxy + C{y^2} \cr
& \frac{{\left( {2x - 3y} \right)\left( {4{x^2} + 6xy + 9{y^2}} \right)}}{{\left( {2x - 3y} \right)}} = A{x^2} + Bxy + C{y^2} \cr
& 4{x^2} + 6xy + 9{y^2} = A{x^2} + Bxy + C{y^2} \cr
& {\text{Comparison both side}} \cr
& A = 4,\,B = 6,\,C = 9 \cr
& \left( {2A + B - C} \right) \cr
& = \left( {2 \times 4 + 6 - 9} \right) \cr
& = 5 \cr} $$
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