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Why (x + 3)² isn't x² + 9

(x + 3)² means (x + 3) times (x + 3). Squaring each piece on its own skips the middle term, and the middle term is where the points go.

Multiply it out

(x + 3)(x + 3) = x·x + x·3 + 3·x + 3·3 = x² + 6x + 9. The 6x is the part that goes missing.

The 5-second check

Put in x = 1. (1 + 3)² = 16, but 1² + 9 = 10. They don't match, so x² + 9 can't be right. With the middle term: 1 + 6 + 9 = 16. ✓

The pattern

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• Example: (2x − 5)² = 4x² − 20x + 25

Solving (x + 3)² = 49

You don't have to expand at all. Take the square root of both sides, and keep both signs: x + 3 = 7 or x + 3 = −7, so x = 4 or x = −10. Forgetting the ± is the second most common slip on this kind of problem.