Final answer:
To find the area of a rectangle in polynomial standard form, we multiply the length and width. In this case, the area is 4x^2-16x+25.
Step-by-step explanation:
The area of a rectangle is found by multiplying its length and width. In this case, the length is (2x+5)(x-1) and the width is (2-3x). To find the area, we use the distributive property to multiply the length and width:
Area = (2x+5)(x-1)(2-3x)
To simplify this expression, we can use the FOIL method to multiply the first terms, outer terms, inner terms, and last terms:
Area = (2x^2-2x+5x-5)(2-3x)
Continuing to simplify, we combine like terms:
Area = (2x^2+3x-5)(2-3x)
Finally, we can use the distributive property again to multiply:
Area = 4x^2-6x-10x+15x+25-15x
Combining like terms once more, we have:
Area = 4x^2-6x-10x+15x+25-15x = 4x^2-16x+25
Therefore, the area of the rectangle in polynomial standard form is 4x^2-16x+25.
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