CPM Homework Help : AC Problem 8-6

Write the area of the rectangle at right as a sum and as a product.

Generic rectangle interior top left $-3x$

interior top middle $-6y$

interior top right $12$

interior bottom left $2x^2$

interior bottom middle $4xy$

interior bottom right $-8x$

Hint 1:

Find the dimensions of the large rectangle.

Hint 2:

To show the area as a product, write the dimensions multiplied together.

Hint 3:

To show the area as a sum, add up all of the tile pieces.

Generic rectangle left edge top $-3$

interior top left $-3x$

interior top middle $-6y$

interior top right $12$

left edge bottom $2x$

interior bottom left $2x^2$

interior bottom middle $4xy$

interior bottom right $-8x$

bottom edge left $x$

bottom edge middle $2y$

bottom edge right $-4$

Answer:

As a product area $= (2x − 3)(x + 2y − 4)$
As a sum area $= 2x^2− 11x + 4xy − 6y + 12$