Given w+10 what is the answer to w+(w-12/2 square *3)*7
To simplify the expression w+(w-12/2)^2*3*7, we can follow the order of operations (also known as PEMDAS) to evaluate it step by step.
1. Start by simplifying the expression within the parentheses (w-12/2). In this case, 12/2 equals 6, so the expression becomes w+(w-6)^2*3*7.
2. Next, square the expression inside the parentheses to get (w-6)^2. Squaring means multiplying the expression by itself, so we have (w-6)*(w-6). This can be simplified to (w-6)^2.
3. Multiply the squared expression by 3 to get 3*(w-6)^2.
4. Multiply the result from step 3 by 7 to get 7*3*(w-6)^2.
Now let's combine these simplified parts together with w+10:
w+(w-6)^2*3*7 can be written as w + 10 + 7*3*(w-6)^2.
This is the simplified expression.
To simplify the expression w + (w - 12/2)^2 * 3 * 7, we can break it down into smaller steps.
Step 1: Simplify w - 12/2
Using the order of operations (PEMDAS), we first divide 12 by 2, which equals 6.
So, w - 12/2 becomes w - 6.
Step 2: Square (w - 6)
To square a value, we multiply it by itself. Therefore, (w - 6)^2 = (w - 6) * (w - 6).
Step 3: Simplify (w - 6) * (w - 6)
We can apply the FOIL method to multiply (w - 6) and (w - 6).
(w - 6) * (w - 6) = w * w - 6 * w - 6 * w + 6 * 6
= w^2 - 12w + 36
Step 4: Multiply (w^2 - 12w + 36) * 3 * 7
Now, we simplify the rest of the expression.
(w^2 - 12w + 36) * 3 * 7
= 3 * 7 * (w^2 - 12w + 36)
= 21 * (w^2 - 12w + 36)
= 21w^2 - 252w + 756
Step 5: Add w + (21w^2 - 252w + 756) to w + 10
Finally, we add w + (21w^2 - 252w + 756) to w + 10.
w + (21w^2 - 252w + 756) + w + 10
= 2w + w + 21w^2 - 252w + 756 + 10
= 22w + 21w^2 - 242w + 766
Therefore, the simplified expression is 21w^2 - 220w + 766.