Question

Find the values for a aa and b bb that would make the equality true. 4 y ( a y 2 − 7 y + b ) = 24 y 3 − 28 y 2 − 8 y 4y(ay 2 −7y+b)=24y 3 −28y 2 −8y

Answer 1

Answer:

a=6, b=-2

Step-by-step explanation:

We are to determine the values for a and b that would make the equality

$4y(ay^2 -7y+b)=24y^3 -28y^2 -8y$ true.

Given:

$4y(ay^2 -7y+b)=24y^3 -28y^2 -8y$

First, we expand the Left Hand Side of the equality

$4y(ay^2 -7y+b)=24y^3 -28y^2 -8y\\4ay^3 -28y^2+4yb=24y^3 -28y^2 -8y$

Comparing coefficients of the same power:

$y^3: 4a=24\\y^2:-28=-28\\y: 4b=-8$

Therefore:

$a= 24 \div 4 =6\\b=-8 \div 4=-2\\a=6, b=-2$