### Home > INT2 > Chapter 2 > Lesson 2.3.1 > Problem2-79

2-79.

Copy each of the area models below and fill in the missing dimensions and areas. Then write the entire area as a product equivalent to the area as a sum.

1.  generic rectangle interior left $2xy$ interior right $8y$ bottom right edge $x$ bottom right edge is blank

Try to find a way to factor what is inside of the boxes, then it is possible to write the area as a product of its sum.

$2xy+8y=2y(x+4)$

1.  generic rectangle interior top left $x^2$ interior top right is blank interior bottom left $8x$ interior bottom right is blank bottom edge left is blank bottom edge right $+5$

$(x+8)(x+5)=x^2+13x+40$

1.  generic rectangle left edge top is blank interior top left is blank interior top middle $-3xy$ interior top right is blank left edge bottom $-4$ interior bottom left$-8z$ interior bottom middle is blank interior bottom right$-20$ bottom edge left is blank bottom edge middle $-3y$ bottom edge right is blank

$(x−4)(2z−3y+5)=2xz-3xy+5x-$
$8z+12y−20$.

1.  generic rectangle left edge right $x$ interior top right $x^2$ interior top right is blank left edge bottom is blank interior bottom left is blank interior bottom right $6$

Multiple answers are possible.