Solve (x+3)(x-3) = x²+x: Expanding Brackets Problem

Q: Why can't I just expand the brackets normally?

You can expand normally, but recognizing the difference of squares pattern saves time! $ (x+3)(x-3) $ instantly becomes $ x^2 - 9 $ instead of doing four multiplications.

Q: How do I know when to use difference of squares?

Look for the pattern (a + b)(a - b) where you have the same terms but opposite signs in the middle. Like $ (x+3)(x-3) $ or $ (2y+5)(2y-5) $.

Q: What happens after I expand the left side?

After getting $ x^2 - 9 = x^2 + x $, subtract $ x^2 $ from both sides to get $ -9 = x $. The $ x^2 $ terms cancel out completely!

Q: Why is the answer negative?

Don't worry about the sign! When we simplified, we got $ -9 = x $, which means $ x = -9 $. Negative solutions are perfectly valid in algebra.

Q: How can I double-check this answer?

Substitute $ x = -9 $ into the original equation: $ (-9+3)(-9-3) = (-6)(-12) = 72 $ and $ (-9)^2 + (-9) = 81 - 9 = 72 $. Both sides equal 72! ✓

Expanding Brackets with Difference of Squares

Solve the following equation:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this problem together.

00:12 We'll use some multiplication shortcuts to simplify the expressi ons inside the brackets.

00:22 Next, we'll find the value of the square and calculate it carefully.

00:28 Let's simplify everything as much as we can.

00:33 And there you have it! We've found the solution to the problem .

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

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

Step-by-step solution

Let's examine the given equation:

$(x+3)(x-3)=x^2+x$ First, let's simplify the equation, for this we'll use the difference of squares factoring formula:

$(a+b)(a-b)=a^2-b^2$ ,

We'll start by opening the parentheses on the left side using the mentioned factoring formula, then we'll move terms, combine like terms, and finally solve the resulting equation:

$(x+3)(x-3)=x^2+x \\ \downarrow\\ x^2-3^2=x^2+x \\ x^2-9=x^2+x \\ x^2-9-x^2-x=0 \\ \boxed{x=-9}$ Therefore, the correct answer is answer B.

Final Answer

$x=-9$

Key Points to Remember

Essential concepts to master this topic

Difference of Squares: $(a+b)(a-b) = a^2 - b^2$ simplifies multiplication
Technique: $(x+3)(x-3) = x^2 - 9$ then move all terms to one side
Check: Substitute $x = -9$ : $(-6)(-12) = 72$ and $81 + (-9) = 72$ ✓

Common Mistakes

Avoid these frequent errors

Expanding brackets by distributing each term separately
Don't expand (x+3)(x-3) as x² + 3x - 3x - 9 = x² - 9! While this gives the correct result, it's much slower. Always recognize the difference of squares pattern (a+b)(a-b) = a² - b² for instant simplification.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

$$ x^2-1=0 $$

FAQ

Everything you need to know about this question

Why can't I just expand the brackets normally?

You can expand normally, but recognizing the difference of squares pattern saves time! $(x+3)(x-3)$ instantly becomes $x^2 - 9$ instead of doing four multiplications.

How do I know when to use difference of squares?

Look for the pattern (a + b)(a - b) where you have the same terms but opposite signs in the middle. Like $(x+3)(x-3)$ or $(2y+5)(2y-5)$ .

What happens after I expand the left side?

After getting $x^2 - 9 = x^2 + x$ , subtract $x^2$ from both sides to get $-9 = x$ . The $x^2$ terms cancel out completely!

Why is the answer negative?

Don't worry about the sign! When we simplified, we got $-9 = x$ , which means $x = -9$ . Negative solutions are perfectly valid in algebra.

How can I double-check this answer?

Substitute $x = -9$ into the original equation: $(-9+3)(-9-3) = (-6)(-12) = 72$ and $(-9)^2 + (-9) = 81 - 9 = 72$ . Both sides equal 72! ✓

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