Question

H(y) = -3y³ - 6y + 9
a. h(4)
b. h(-2y)
c. h(5b + 3)

Answer 1

a. h(4) = -207

b. h(-2y) = 24y³ +12y +9

c. h(5b+3) = -375b³ -675b² -435b -90

Explanation:

You want the simplified form of h(y) = -3y³ -6y +9 for using 3 different values of y.

The expression is evaluated by putting the argument where y is, then simplifying the resulting expression.

a. h(4)

`h(4)=-3(4)^3 -6(4) +9 = -3(64) -24 +9\\\\\boxed{h(4) = -207}`

b. h(-2y)

`h(-2y)=-3(-2y)^3-6(-2y)+9=-3(-8y^3+12y+9\\\\\boxed{h(-2y)=24y^3+12y+9}`

c. h(5b+3)

`h(5b+3)=-3(5b+3)^3-6(5b+3)+9=-3(125b^3+225b^2+135b +27) -30b-18+9\\\\\boxed{h(5b+3)=-375b^3-675b^2-435b-90}`

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Additional comment

It can be useful to remember that ...

(a +b)³ = a³ +3a²b +3ab² +b³