Find the Missing Term in the Equation: x² + ? + 9 = (x + 3)²

Fill in the blanks:

$x^2+\text{?}+9=(x+3)^2$

To solve this problem, let's start by expanding the expression on the right side of the equation using the formula for the square of a sum.

Step 1: Expand $(x + 3)^2$:

• Using the formula $(a + b)^2 = a^2 + 2ab + b^2$, we substitute $a = x$ and $b = 3$.
• We have: $(x + 3)^2 = x^2 + 2 \times x \times 3 + 3^2$.
• Simplifying, we get: $x^2 + 6x + 9$.

Step 2: Compare with the given expression:

• The left side of the equation is $x^2 + \text{?} + 9$.
• From our expansion, we see $x^2 + 6x + 9$ matches the structure $x^2 + \text{?} + 9$.
• This implies the missing term $\text{?}$ is $6x$.

Therefore, the missing term in the expression $x^2 + \text{?} + 9 = (x + 3)^2$ is $6x$.