What does it mean to equate two expressions?

Question

it says that in a math problem i have for my summer work. here's the problem:

Use the area model to write two expressions for the total area in the figure. Then, equate the two expressions and name the algebraic property illustrated.

diagram: http://img153.imageshack.us/img153/7819/34055136fh2.jpg

^^on the top is a x and a 5. on the side is a x and a 3.

thanks for any help.

Answer 1

One way of writing the area of the figure is (x + 5)(x + 3). Another way is to add up the little areas: x*x + 3*x + 5*x + 3*5. Since the areas are equal, equate both expressions for the area: (x + 5)(x + 3) = x^2 + 8x + 15.

The property illustrated is called the distributive property of multiplication over addition.

Answer 2

You can do the product of (x+3) and (x+5) to get the area or go at it piecemeal as the sum of the 3 rectagles and the x*x square.   It has to do with multiplicative properties.