Question
A group of art students are painting a mural on a wall. The rectangular wall has dimensions of (6x + 7) by (8x + 5) and they are planning the mural to be (x + 4) by (2x + 5). What is the area of the remaining wall after the mural has been painted?
Answers
GPT 3.5
The area of the rectangular wall is (6x + 7)(8x + 5).
The area of the planned mural is (x + 4)(2x + 5).
The area of the remaining wall is the difference between these two areas, which is (6x + 7)(8x + 5) - (x + 4)(2x + 5).
Expanding the expressions, we get 48x^2 + 82x + 35 - 2x^2 - 5x - 20.
Combining like terms, we get 46x^2 + 77x + 15.
So the area of the remaining wall is 46x^2 + 77x + 15. Answer: \boxed{46x^2 + 77x + 15}.
The area of the planned mural is (x + 4)(2x + 5).
The area of the remaining wall is the difference between these two areas, which is (6x + 7)(8x + 5) - (x + 4)(2x + 5).
Expanding the expressions, we get 48x^2 + 82x + 35 - 2x^2 - 5x - 20.
Combining like terms, we get 46x^2 + 77x + 15.
So the area of the remaining wall is 46x^2 + 77x + 15. Answer: \boxed{46x^2 + 77x + 15}.
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