# 1.2 Modeling Algebraic Expressions using tiles

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1.2 Modeling Algebraic Expressions using tiles

Which algebraic expression can be found of the next figure?
What does the a represent? and b? and c? What kind of polygon has the area : A = ab + ac? c b Using the formula A= base X height, the area of any rectangle can be calculate base = a, height = b + c Area = a X ( b + c ) The expression (b+ c) indicates that this addition must be solved first and the sum should be multiplied by a. In this case, the multiplication sign can be omitted and writen as: A = a(b+c) a

1. How can the area of one of the rectangles be represented?
2. If you add the areas made by the next three rectangles, how can you write the expression that represents the total area? x

Use the rectangle below to explain the next equality: 5(x + 4) = 5x + 20

Now, try to explain the next equality: 11(x – 7) = 11x - 77

Draw the rectangles that represent the next equalities
9( x + 6) = 9x + 54 8(x – 4 ) = 8x - 32

As you noticed, parenthesis are used to indicate which operation must be solved first.

Exercises: Sebastian: Raise a number to the second power and then subtract 2, divide the difference by 5. Hortensia: Raise a number to the second power,divide it by 5, and then subract 2. Margarita: Raise a number to the second power and then subtract the quotient of 2 over 5 Can you tell which is Sebastian’s card, Hortensia’s card and Margarita’s card?

Write as an algebraic expression
Eight times the difference of x and y Nine times the difference of y and z, increased by 3z Three times the sum of a and b, decreased by 7a

Match the algebraic expression with its equality
4((x – 2) -8) a) 4x-10 4(x-2) -8 b) 4x-16 (4x-2-8) c) 4x-40