Factorise: 8𝑦2−18𝑦−5

To factorise the quadratic equation 8y^2 - 18y - 5, we need to follow these steps:

Step 1: Multiply the coefficient of y^2 (which is 8) with the constant term (which is -5). This gives us -40.

Step 2: Now, we need to find two numbers that multiply to -40 and add up to -18 (the coefficient of y). The numbers that satisfy these conditions are -20 and 2.

Step 3: Rewrite the middle term of the quadratic equation as the sum of the terms -20y and 2y. This gives us: 8y^2 - 20y + 2y - 5.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us: 4y(2y - 5) + 1(2y - 5).

Step 5: Notice that (2y - 5) is a common factor. We can factor that out, giving us the final factorised form of the equation: (2y - 5)(4y + 1).

So, 8y^2 - 18y - 5 = (2y - 5)(4y + 1).