Complete the Perfect Square: (□×x-□)² = 9x²-24x+16

Video Solution

Solution Steps

00:09 Let's fill in the missing part together.

00:13 Remember the shortcut for multiplying. We'll use these formulas to open up the brackets.

00:20 For the first term, find its square root. Easy, right?

00:25 Now, let's do the same for the last term.

00:32 Break down the middle term into factors: two, three, and four. You got this!

00:43 Next, let's check if the multiplication is correct.

00:48 Substitute each number carefully in its right place.

00:52 Great job! That's how we find the solution to the question.

Step-by-Step Solution

To solve this problem, let's identify the steps needed to determine the missing values.

Step 1: Apply the perfect square formula.
Write $(a \times x - b)^2 = a^2x^2 - 2abx + b^2$ .
Step 2: Compare with the given polynomial.
Set the expression equal to the provided polynomial: $9x^2 - 24x + 16$ .
Step 3: Match coefficients.
From $a^2x^2 = 9x^2$ , we get $a^2 = 9$ .
From $-2abx = -24x$ , we get $-2ab = -24$ .
From $b^2 = 16$ , we get $b^2 = 16$ .
Step 4: Solve for $a$ and $b$ .
- Solve $a^2 = 9$ , giving $a = 3$ or $a = -3$ . Choose $a = 3$ for simplicity.
- Solve $b^2 = 16$ , giving $b = 4$ or $b = -4$ . Choose $b = 4$ for simplicity.
- Check $-2ab = -24$ : $-2(3)(4) = -24$ , which is correct.

Therefore, the missing values are $\boxed{3, 4}$ .

Thus, the solution to the problem is: $3, 4$ .