Factorise y2+40y+400

To factorise the quadratic equation y^2 + 40y + 400, we need to find two numbers that multiply to 400 and add to 40.

Step 1: Identify the coefficient of y^2, y and the constant term. Here, the coefficient of y^2 is 1, the coefficient of y is 40 and the constant term is 400.

Step 2: Find two numbers that multiply to 400 (the constant term) and add to 40 (the coefficient of y). The numbers are 20 and 20 because 20*20 = 400 and 20 + 20 = 40.

Step 3: Rewrite the middle term of the quadratic equation as the sum of the products of the two numbers and y. So, y^2 + 40y + 400 becomes y^2 + 20y + 20y + 400.

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 (y^2 + 20y) + (20y + 400).

Step 5: Factor out the greatest common factor from each group. From the first group, we can factor out y, and from the second group, we can factor out 20. This gives us y(y + 20) + 20(y + 20).

Step 6: Notice that (y + 20) is a common factor. So, we can factor that out to give us (y + 20)(y + 20).

So, the factorised form of y^2 + 40y + 400 is (y + 20)^2.