Question

Write as a polynomial:
a) y^2(y+5)(y-3)
b) 2a^2(a-1)(3-a)

Answer 1

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

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

Answer 2

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

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

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