Question

lins expression: 40y + 40(20)
noahs expression: 40(y + 20)
first, describe lins expression.
write a different expression to find the area of the training center.

Explanation:

Step1: Analyze Lin's expression

Lin's expression \(40y + 40(20)\) represents the sum of the area of the yard (\(40y\)) and the area of the arena (\(40\times20\)).

Step2: Analyze Noah's expression

Noah's expression \(40(y + 20)\) uses the distributive property \(a(b + c)=ab+ac\) (here \(a = 40\), \(b=y\), \(c = 20\)). It considers the combined length (\(y + 20\)) and width (\(40\)) of the whole figure (yard + arena) as a single rectangle.

Step3: Write a different expression

We can also use the commutative property. For example, \(20\times40+40y\) (same as Lin's but with terms reversed) or \((y + 20)\times40\) (same as Noah's). Another way is to expand Noah's expression using distributive property: \(40y+800\) (since \(40\times20 = 800\))

Answer:

Lin's expression \(40y + 40(20)\) finds the sum of two areas (yard and arena). Noah's expression \(40(y + 20)\) uses the distributive property for a single - rectangle view. A different expression could be \(40y+800\) (by calculating \(40\times20\) in Lin's expression).