Write as a polynomial:

a) y^2 (y+5) (y-3)

b) 2a^2 (a-1) (3-a)

Answer: (a) y⁴ + 2y³ - 15y², (b) - 2a⁴ + 8a³ - 6a²

Step-by-step explanation:

(a) y²{ (y + 5) (y - 3) }, open the brackets in the bigger brackets, and then use the y² to open the brackets.

y² (y² - 3y + 5y - 15)

y² (y² + 2y - 15)

y⁴ + 2y³ - 15y²

Performe same operation here

(b) 2a² { (a - 1) (3 - a) }

2a² (3a - a² - 3 + a)

2a² (4a - a² - 3)

2a² (-a² + 4a - 3)

-2a⁴ + 8a³ - 6a²

a) y^4 + 2y^3 - 15y^2

b) - 2a^4 + 8a^3 - 6a^2

Step-by-step explanation:

It is convenient to multiply the binomials first. The distributive property applies.

a) y^2 (y (y - 3) + 5 (y - 3)) = y^2 (y^2 - 3y + 5y - 15) = y^4 + 2y^3 - 15y^2

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b) 2a^2 (a (3 - a) - 1 (3 - a)) = 2a^2 (3a - a^2 - 3 + a) = - 2a^4 + 8a^3 - 6a^2