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Chapter 0: Problem 80

Find each product. $$(x+y+2)^{2}$$

Short Answer

Expert verified
The expansion of \( (x+y+2)^{2} \) is \( x^{2} + 2xy + y^{2} + 4x + 4y + 4 \)

Step by step solution

01

Binomial expansion

A binomial expression raised to the power 2 can be expanded according to the binomial theorem as \( (a+b)^{2} = a^{2} + 2ab + b^{2} \). Now, substiute \( x+y \) for \( a \) and 2 for \( b \) in the formula. So, it becomes \( (x+y)^{2} + 2 * (x+y) * 2 + 2^{2} \)
02

Expand the terms individually

Now expand each term individually. Expanding \( (x+y)^{2} \) gives \( x^{2} + 2xy + y^{2} \). Then calculate \( 2 * (x+y) * 2 \) using distribution, which gives \( 4x + 4y \), and finally compute \( 2^{2} = 4 \)
03

Adding the terms

Combine all the terms to get the final expanded form of the given equation. The final expression will be \( x^{2} + 2xy + y^{2} + 4x + 4y + 4 \)

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