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

Video Solution

Solution Steps

00:00 Complete the missing part

00:03 We'll use the shortened multiplication formulas to find the brackets

00:11 We'll break down the first term into its square root

00:16 We'll do the same for the last term

00:23 We'll break down the middle term into factors 2, 3, and 4

00:34 We'll verify that the multiplication is correct

00:38 We'll substitute the numbers in their correct places

00:43 And this is 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: $3, 4$ .