Factorise y2+8y+16 completely.

To factorise the quadratic equation y^2 + 8y + 16 completely, we need to find two numbers that multiply to 16 and add to 8.

Step 1: Identify the numbers The numbers that satisfy these conditions are 4 and 4, because 4*4 = 16 and 4+4 = 8.

Step 2: Rewrite the equation We can rewrite the equation as y^2 + 4y + 4y + 16.

Step 3: Factor by grouping Now, we can factor by grouping. The first two terms, y^2 + 4y, can be factored to y(y + 4). The last two terms, 4y + 16, can be factored to 4(y + 4).

Step 4: Combine like terms Since both terms are now the same (y + 4), we can combine them to get (y + 4)^2.

So, the factorised form of y^2 + 8y + 16 is (y + 4)^2.