Question
Evaluate: $(3x - 2y)(4x + 3y) (8x - 5y)$
✓
Answer
$(3x - 2y)(4x + 3y)(8x - 5y)$
$= 3x (4x + 3y) - 2y (4x + 3y)(8x - 5y)$
$= (12x^2 + 9xy - 8xy - 6y^2)(8x - 5y)$
$= (12x^2 + xy - 6y^2 )(8x - 5y)$
$= 8x (12x^2 + xy - 6y^2 ) - 5y (12x^2 + xy - 6y^2 )$
$= 96x^3 + 8x^2y - 48xy^2 - 60x^2y - 5xy^2 + 30y^3$
$= 96x^3 + 8x^2y - 60x^2y - 48xy^2- 5xy^2 + 30y^3$
$= 96x^3 - 52x^2y - 53xy^2 + 30y^3$
$= 3x (4x + 3y) - 2y (4x + 3y)(8x - 5y)$
$= (12x^2 + 9xy - 8xy - 6y^2)(8x - 5y)$
$= (12x^2 + xy - 6y^2 )(8x - 5y)$
$= 8x (12x^2 + xy - 6y^2 ) - 5y (12x^2 + xy - 6y^2 )$
$= 96x^3 + 8x^2y - 48xy^2 - 60x^2y - 5xy^2 + 30y^3$
$= 96x^3 + 8x^2y - 60x^2y - 48xy^2- 5xy^2 + 30y^3$
$= 96x^3 - 52x^2y - 53xy^2 + 30y^3$
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