Perfect Square Expansion: Find the Missing Term in x² + ? + 9 = (x-3)²

Fill in the blanks:

$x^2+?+9=(x-3)^2$

To address this mathematical problem, we will apply the square of a binomial formula and solve for the missing term. Here's how:

• Step 1: Expand the right-hand side of the equation $(x-3)^2$.
• Step 2: Equate the expanded form to $x^2 + ? + 9$.
• Step 3: Solve for the missing term by comparing the coefficients.

Step 1: Expanding $(x-3)^2$ using the formula, we get:

$(x - 3)^2 = x^2 - 2 \cdot x \cdot 3 + 3^2$.

This simplifies to:

$x^2 - 6x + 9$.

Step 2: Equating this to the left-hand side:

$x^2 + ? + 9 = x^2 - 6x + 9$.

Step 3: Compare the terms:

The term that replaces "?" on the left-hand side must make the equation hold.

Setting corresponding terms equal, we find that:

$? = -6x$.

Therefore, the solution to the problem is $-6x$.