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Hello. My middle-school son has what appears to be a simple problem, but I'm just too rusty in my algebra to recall how to solve it.

The problem involves writing expressions, one in factored form and one in expanded form, for the area of a rectangle of sides x+2 and x+3. We've gotten as far as area = (x+2)(x+3). But I can't come up with the other expression.

Your help would be greatly appreciated.

Best,
Rick
 

 

Hi Rick,

The expansion comes from what your son probably learned as the distributive law. That is

a (b + c) = a b + a c

This is also true if the multiplication is on the right

(b + c) a = b a + c a

This just says that you can evaluate 3 (5 + 2) as 3 7 = 21 or 3 5 + 3 2 = 15 + 6.

If you apply this to (x + 2)(x + 3) you get

(x + 2)(x + 3)
= (x + 2) x + (x + 2) 3

Now apply the distributive law with multiplication on the right

(x + 2)(x + 3)
= (x + 2) x + (x + 2) 3
= x x + 2 x + x 3 + 2 x
= x2 + 5x + 6

Penny

 
 

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