Let's learn how to factor $x^2 - 9$! 🎉
1️⃣ Imagine you have a square with side length $x$. That means the area is $x^2$.
Square area:
⬛
($x^2$)
2️⃣ Now think about 9 as a smaller square with side length 3. So its area is $3^2=9$. ⬛
($x^2$)
Small square:
🟦🟦🟦
🟦🟦🟦
🟦🟦🟦
(9)
3️⃣ $x^2 - 9$ is a difference of squares because it looks like $a^2 - b^2$. Here, $a=x$ and $b=3$.
4️⃣ The formula is: $$a^2 - b^2 = (a - b)(a + b)$$
5️⃣ So, $x^2 - 9 = (x - 3)(x + 3)$.
6️⃣ Great! Let's see it as groups:
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🟦🟦🟦
🟦🟦🟦
(9)
Group 1:
❌ ❌ ❌
(x - 3)
➕
❌ ❌ ❌
(x - 3)
Group 2:
❌ ❌ ❌ ❌
(x + 3)
That's the answer! 🎯
Final answer: $$x^2 - 9 = (x - 3)(x + 3)$$❌ ❌ ❌ ❌
(x + 3)