A rectangular cage is being constructed with side lengths $(3 x-1) \mathrm{ft}$ and $(-4 x+1) \mathrm{ft}$. A student is attempting to find an expression for the cage's area using algebra tiles, but his work is incorrect. Point out each mistake by clicking on every tile that is incorrect in the diagram.
Answer
Thus, the correct expression for the area of the rectangular cage is \(\boxed{-12x^2 + 7x - 1}\).
Step 1 ：The problem provides the lengths of the sides of a rectangular cage as \((3x - 1)\) ft and \((-4x + 1)\) ft.
Step 2 ：We are asked to find an expression for the area of the cage.
Step 3 ：The area of a rectangle is given by the product of its length and width.
Step 4 ：So, we multiply the expressions for the length and width to find the area: \((3x - 1) * (-4x + 1)\).
Step 5 ：Solving this, we get the expression for the area as \(-12x^2 + 7x - 1\).
Step 6 ：Thus, the correct expression for the area of the rectangular cage is \(\boxed{-12x^2 + 7x - 1}\).
