Final answer:
The area of the rectangular rug is obtained by multiplying the given length and width, and simplifying the resulting expression. In this case, it simplifies to 30x^(5) - 10x^(4) + 59x^(3) - 8x^(2) + 28x.
Step-by-step explanation:
In mathematics, the area of a rectangle is found by multiplying the length by the width. Given the length of the rug is 5x^(3)+4x and the width is 6x^(2)-2x+7, we multiply these two expressions together to find the area.
The area (A) of the rug can therefore be expressed as:
A = (5x^(3)+4x) * (6x^(2)-2x+7)
This is equivalent to multiplying out the brackets which gives:
A = 30x^(5) - 10x^(4) + 35x^(3) + 24x^(3) - 8x^(2) + 28x
This simplifies to:
A = 30x^(5) - 10x^(4) + 59x^(3) - 8x^(2) + 28x
This is the simplest form of the area of the rug.
Learn more about Area of a Rectangle