Simplify the Quadratic Expression: 9x²-12x+4

Q: How do I know if an expression is a perfect square trinomial?

Look for the pattern $ a^2 \pm 2ab + b^2 $. The first and last terms must be perfect squares, and the middle term must equal $ \pm 2ab $ where a and b are the square roots of the first and last terms.

Q: What if I can't find perfect square roots?

If $ 9x^2 $ doesn't give you a nice square root, or if $ 4 $ isn't a perfect square, then it's probably not a perfect square trinomial. Try other factoring methods like grouping or the quadratic formula.

Q: Why does the middle term have a negative sign?

The middle term's sign depends on the binomial form. For $ (a-b)^2 $, you get $ -2ab $ (negative). For $ (a+b)^2 $, you get $ +2ab $ (positive). The original expression tells you which form to use.

Q: Can I use this method for any quadratic?

No! This only works for perfect square trinomials. Most quadratics like $ x^2 + 5x + 6 $ aren't perfect squares and need different factoring techniques like finding two numbers that multiply and add correctly.

Q: How do I expand to check my answer?

Use FOIL: $ (3x-2)^2 = (3x-2)(3x-2) $. First: $ 3x \cdot 3x = 9x^2 $, Outer + Inner: $ 3x(-2) + (-2)(3x) = -12x $, Last: $ (-2)(-2) = 4 $.

Perfect Square Trinomials with Factoring

$9x^2-12x+4=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:05 Square root is the number itself

00:20 Let's factor 12 into 2 and 6

00:25 Square root is the number itself

00:37 Calculate the root of 9 and X squared

00:43 Calculate root of 4

00:57 Let's factor 6 into 2 and 3

01:16 Use the root formula to find the multiplication

01:23 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$9x^2-12x+4=$

Step-by-step solution

To rewrite the expression $9x^2 - 12x + 4$ as a perfect square, follow these steps:

Step 1: Compare the expression $9x^2 - 12x + 4$ with $(a - b)^2$ .
Step 2: Note that $(a - b)^2 = a^2 - 2ab + b^2$ .
Step 3: Identify matching terms: $a^2 = 9x^2$ , $-2ab = -12x$ , $b^2 = 4$ .

Now, separate this into steps:
Step 1: Set $a^2 = 9x^2$ , so $a = 3x$ .
Step 2: Set $b^2 = 4$ , so $b = 2$ .
Step 3: Verify $-2ab = -12x$ :
$-2 \times 3x \times 2 = -12x.$
This confirms our values of $a$ and $b$ are correct.

Thus, the expression $9x^2 - 12x + 4$ is equivalent to the square $(3x - 2)^2$ .

The correct choice is: $(3x-2)^2$ .

Final Answer

$(3x-2)^2$

Key Points to Remember

Essential concepts to master this topic

Pattern: Perfect squares follow $a^2 - 2ab + b^2 = (a-b)^2$ formula
Technique: Match terms: $9x^2 = (3x)^2$ , $4 = 2^2$ , verify middle term
Check: Expand $(3x-2)^2 = 9x^2 - 12x + 4$ matches original ✓

Common Mistakes

Avoid these frequent errors

Guessing factors without verifying the middle term
Don't assume $(3x-3)^2$ works just because $9x^2$ and constant look right = wrong middle term! Expanding gives $9x^2 - 18x + 9$ , not $-12x$ . Always verify that $-2ab$ equals the middle term exactly.

Practice Quiz

Test your knowledge with interactive questions

Declares the given expression as a sum

$$ (7b-3x)^2 $$

FAQ

Everything you need to know about this question

How do I know if an expression is a perfect square trinomial?

Look for the pattern $a^2 \pm 2ab + b^2$ . The first and last terms must be perfect squares, and the middle term must equal $\pm 2ab$ where a and b are the square roots of the first and last terms.

What if I can't find perfect square roots?

If $9x^2$ doesn't give you a nice square root, or if $4$ isn't a perfect square, then it's probably not a perfect square trinomial. Try other factoring methods like grouping or the quadratic formula.

Why does the middle term have a negative sign?

The middle term's sign depends on the binomial form. For $(a-b)^2$ , you get $-2ab$ (negative). For $(a+b)^2$ , you get $+2ab$ (positive). The original expression tells you which form to use.

Can I use this method for any quadratic?

No! This only works for perfect square trinomials. Most quadratics like $x^2 + 5x + 6$ aren't perfect squares and need different factoring techniques like finding two numbers that multiply and add correctly.

How do I expand to check my answer?

Use FOIL: $(3x-2)^2 = (3x-2)(3x-2)$ . First: $3x \cdot 3x = 9x^2$ , Outer + Inner: $3x(-2) + (-2)(3x) = -12x$ , Last: $(-2)(-2) = 4$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Short Multiplication Formulas questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime