Question
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2.) \( [x-y+3]^{2} \)

Ask by Ryan Coleman. in South Africa
Feb 03,2025

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Answer

The expanded form of \( [x - y + 3]^2 \) is \( x^{2} - 2xy + 6x + y^{2} - 6y + 9 \).

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The Deep Dive

Let's unpack this expression a bit! When you see \( [x-y+3]^{2} \), it’s like a little treasure chest waiting to be opened! This is actually a perfect square trinomial. To expand it, you'll apply the formula \( (a+b)^{2} = a^{2} + 2ab + b^{2} \). Here, you can think of \( a = x-y \) and \( b = 3 \), leading us to \( (x-y)^{2} + 2(x-y)(3) + 3^{2} \). Also, a common mistake when squaring binomials (like yours!) is forgetting to apply the distributive property to each term. Some may just square the first term and the last term, but the middle term—where the two components interact—holds the magic! So remember to bring your A-game to those brackets!

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