Factorise 16w2+24w+9 completely.

Sure, here is the step-by-step solution:

Step 1: Identify the expression The given expression is 16w^2 + 24w + 9.

Step 2: Recognize the pattern This is a quadratic equation in the form of ax^2 + bx + c. Here, a = 16, b = 24, and c = 9.

Step 3: Factorise We need to factorise the equation in the form of (dw + e)^2.

Step 4: Find the square root of a and c The square root of 16 (a) is 4 and the square root of 9 (c) is 3. So, d = 4 and e = 3.

Step 5: Check if 2de equals to b 243 = 24, which is equal to b.

Step 6: Write the factorised form So, the factorised form of the equation is (4w + 3)^2.