Simplify (5 – x) (3 – 2x) (4 – 3x).

1.	Simplify (5 – x) (3 – 2x) (4 – 3x).
Answer» (5 – x) (3 – 2x) (4 – 3x) = {(5 – x)(3 – 2x)} × (4 – 3x) [∴ Multiplication in association] = {5 (3 – 2x) -x (3 – 2x)} × (4 – 3x) = (15 – 10x – 3x + 2x²) × (4 – 3x) = (2x² – 13x + 15) (4 – 3x) = 2x² × (4 – 3x) – 13x (4 – 3x) + 15 (4 – 3x) = 8x³ – 6³ – 52x + 39x² + 60 – 45x = -6x³ + 47x² – 97x + 60

Answer»

(5 – x) (3 – 2x) (4 – 3x)

= {(5 – x)(3 – 2x)} × (4 – 3x) [∴ Multiplication in association]

= {5 (3 – 2x) -x (3 – 2x)} × (4 – 3x)

= (15 – 10x – 3x + 2x²) × (4 – 3x)

= (2x² – 13x + 15) (4 – 3x)

= 2x² × (4 – 3x) – 13x (4 – 3x) + 15 (4 – 3x)

= 8x³ – 6³ – 52x + 39x² + 60 – 45x

= -6x³ + 47x² – 97x + 60

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