Simplify:(5y + 1)(5y + 2)(5y + 3)

1.	Simplify:(5y + 1)(5y + 2)(5y + 3)
Answer» (5y + 1) (5y + 2) (5y + 3) Comparing (5y + 1) (5y + 2) (5y + 3) with (x + a) (x + b) (x + c) we have x = 5y ; a = 1; b = 2 and c = 3. (x + a) (x + b) (x + c) = x³ + (a + b + c) x² (ab + bc + ca) x + abc = (5y)³ + (1 + 2 + 3) (5y)² + [(1) (2) + (2) (3) + (3) (1)] 5y + (1)(2) (3) = 5³y³ + 6(5²y²) + (2 + 6 + 3)5y + 6 = 125³ + 150y² + 55y + 6

Answer»

(5y + 1) (5y + 2) (5y + 3)

Comparing (5y + 1) (5y + 2) (5y + 3) with (x + a) (x + b) (x + c) we have x = 5y ; a = 1; b = 2 and c = 3.

(x + a) (x + b) (x + c) = x³ + (a + b + c) x² (ab + bc + ca) x + abc

= (5y)³ + (1 + 2 + 3) (5y)² + [(1) (2) + (2) (3) + (3) (1)] 5y + (1)(2) (3)

= 5³y³ + 6(5²y²) + (2 + 6 + 3)5y + 6

= 125³ + 150y² + 55y + 6

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