Final answer:
The area of the rectangle with a height of 7 and a width of 3x² + 8z + 7 is 21x² + 56z + 49 when expressed as a polynomial in standard form.
Step-by-step explanation:
To express the area of a rectangle, you simply multiply the height by the width. In this case, our rectangle has a height of 7-12 and a width of 3x² + 8z + 7. However, the height given seems to have a typo and should likely be a single term. If we assume the height is actually 7, and ignore the -12 as a typo, we can multiply the height (7) by the width (3x² + 8z + 7).
The area of the rectangle is 7(3x² + 8z + 7), which simplifies to:
21x² + 56z + 49
This is the polynomial that represents the area of the entire rectangle in standard form.