Answer:
a=6, b=-2
Step-by-step explanation:
We are to determine the values for a and b that would make the equality
[tex]4y(ay^2 -7y+b)=24y^3 -28y^2 -8y[/tex] true.
Given:
[tex]4y(ay^2 -7y+b)=24y^3 -28y^2 -8y[/tex]
First, we expand the Left Hand Side of the equality
[tex]4y(ay^2 -7y+b)=24y^3 -28y^2 -8y\\4ay^3 -28y^2+4yb=24y^3 -28y^2 -8y[/tex]
Comparing coefficients of the same power:
[tex]y^3: 4a=24\\y^2:-28=-28\\y: 4b=-8[/tex]
Therefore:
[tex]a= 24 \div 4 =6\\b=-8 \div 4=-2\\a=6, b=-2[/tex]
