Question

The rectangle shown below has an area of 4(x+3) square units.
A. Use the distributive property to write an equivalent expression for the rectangle's are.
B. If both of the dimensions of the original rectangle are doubled, what is the area of the new rectangle in terms of x?

Answer 1

Remark

The area = 4*(x + 3) to start with. If you remove the brackets,

A = 4(x + 3)

A = 4*x + 3*4

A = 4x + 12 <<<<<< Answer for A

Part B

The area will become 4 times larger.

A = 4*(4x + 12)

A = 16x + 48

Argument

You may not be wholly satisfied with an unproved statement. I could prove it with algebra but it might be easier just to give an example.

Area = L * W

L = 10

W = 5

Area = 10*5

Area = 50

Now double both L and W

L = 20

W = 10

Area = L*W

Area = 20*10

Area = 200 which is 4 times the size of 50.