Question

The table shows the area of two rugs a preschool teacher has in her room. She places the two rugs together to make one big rug.

Rug Area
(square units)
Blue 8(x+12)
Red 10(x+25)

What is the area in square units of the new rug, in factored form?

__ square units

1. By adding the area of the given two rugs together and from the distributive property of multiply the constant we get the area of the new rug in factored form = 2(9x + 173) square units.

### What is factored form?

When an expression is represented as a product of its factors it is considered as a factored form.

### What is distributive property of multiply by constant?

The distributive property is a property of arithmetic that states that multiplying a number by a group of numbers is the same as multiplying each number in the group by the number individually and then adding the products together.
Blue rug: 8(x+12)
Red rug: 10(x+25)
New rug: 8(x+12) + 10(x+25)
Next, we can use the distributive property to multiply the constants and the parentheses:
New rug: 8(x+12) + 10(x+25)
New rug: 8x + 96 + 10x + 250
Then we can combine like terms:
New rug: 8x + 96 + 10x + 250
New rug: 18x + 346
Finally, we can factor the expression to get:
New rug: 18x + 346
New rug: 2(9x + 173)
So the area of the new rug is 2(9x + 173) square units.