Question

"Find the values for a and b that would make the equality true. -2y(y– 6y - 3) = ay} + 12y2 + by a= b="

Answer 1

The values for a and b that make the equality true, let's simplify the equation and solve the system of equations obtained by grouping the terms. The values for a and b that make the equality true are a = -2 and b = 8.

The corrected equation is -
`2y(y - 6y - 3) = ay + 12y^2 + by`.

To find the values for a and b that make the equality true, let's simplify the equation:

`-2y(-5y - 3) = ay + 12y^2 + by`

Distribute the -2y on the left side:

`10y^2 + 6y = ay + 12y^2 + by`

Now, let's group the terms:

`10y^2 + 6y = (a + 12)y^2 + (a + b)y`

For the equality to hold true, the coefficients of corresponding powers of y on both sides must be equal. This gives us a system of equations:

Coefficients of
`y^2: 10 = a + 12`

Coefficients of
`y: 6 = a + b`

Solving these two equations will give us the values for a and b:

a + 12 = 10 ⟶ a = -2

a + b = 6 ⟶ -2 + b = 6 ⟶ b = 8

Therefore, the values for a and b that make the equality true are

a = -2 and b = 8.