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Add a constant term to the expression to convert it to a perfect square. Question 5, 1.3.33

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mework Add a constant term to the expression to convert it to a perfect square. Question 5, 1.3.33 $$ y^{2}+12 \mathrm{y} $$

UpStudy AI · Accepted Answer

To convert the expression $$ y^{2} + 12y $$ into a perfect square, you need to **complete the square** by adding an appropriate constant term. Here's a step-by-step guide to doing this:

### Step 1: Start with the Given Expression
$$ y^{2} + 12y $$

### Step 2: Identify the Coefficient of $$ y $$
The coefficient of $$ y $$ is **12**.

### Step 3: Calculate Half of the Coefficient
$$ \frac{12}{2} = 6 $$

### Step 4: Square This Half
$$ 6^{2} = 36 $$

### Step 5: Add This Square to the Original Expression
By adding **36**, the expression becomes:
$$ y^{2} + 12y + 36 $$

### Step 6: Write the Perfect Square
The resulting expression is a perfect square:
$$ y^{2} + 12y + 36 = (y + 6)^{2} $$

### Conclusion
The **constant term** you need to add to $$ y^{2} + 12y $$ to make it a perfect square is **36**.

**Final Answer:**
$$ y^{2} + 12y + 36 = (y + 6)^{2} $$

Thus, **36** is the constant term required to complete the square.
To make $$ y^{2} + 12y $$ a perfect square, add **36**.

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Add a constant term to the expression to convert it to a perfect square. Question 5, 1.3.33

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