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If 27x3 - 64y3 = (Ax + By) (Cx2 - Dy2...

This question belongs to Arithmetic Ability Algebra
Algebra
?

If 27x3 - 64y3 = (Ax + By) (Cx2 - Dy2 + 12xy) then the value of 4A + B + 3C + 2D is:

Answer & Solution
Correct Answer: Option D
27x3 - 64y3
= (3x)3 - (4y)3
= (3x - 4y)[(3x)2 + (4y)2 + 3x × 4y]
= (3x - 4y)[9x2 + 16y2 + 12xy]
= (Ax + By) (Cx2 - Dy2 + 12xy)
Compare value A, B, C, D
A = 3; B = -4; C = 9; D = -16
4A + B + 3C + 2D
= 4 × 3 + (-4) + 3 × 9 + 2 × (-16)
= 12 - 4 + 27 - 32
= 3
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