Question

Each expression below represents the area of a rectangle written as a product dength)(width Sketch an area model for each expression on your paper and label its length and width. Then write an equation showing that the area written as a product is equal to the area written as the sum of the parts. Be prepared to share your equations with the class. a. (x+3)(2x + 1) b. 2x(x + 5) 2 3 c. x(2x - y) d. (2x + 5)(x + y + 2) (26 - 1))+ (2x-1) (2x-1) 1. (2x)(4x) h. y(2x + y + 3) 5) g. 2(3x 2

Answer 1

We have to write an equation showing that the area written as a product is equal to the area written as the sum of the parts.

The expression is:

$(2x+5)(x+y+2)$

We can show it graphically as:

If we apply the distributive property to the expression, we get:

$\begin{gathered} (2x+5)(x+y+2) \\ 2x\mleft(x+y+2\mright)+5\mleft(x+y+2\mright) \\ 2x^2+2xy+4x+5x+5y+10 \end{gathered}$

The terms of the sum are the areas of the triangles shown in the drawing.

Answer:

(2x+5)(x+y+2) = 2x^2+2xy+4x+5x+5y+10 = 2x^2+2xy+9x+5y+10