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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.

   To learn more about arithematic expression visit:

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