Question

Part a: The student made a mistake in the second step. He was supposed to open the bracket with the minus sign. Part b: Let's correct the mistakes and solve them accordingly. Step 1: 12(8x - 4y) - 3(12y - 9x). Step 2: 96x - 48y - 36y - 27x. Step 3: 96x - 27x - 48y - 36y. Step 4: (96x - 27x)(-48y - 36y). Step 5: 69x - 84y.

Answer 1

The student's mistake was corrected by properly distributing the negative sign and then combining like terms, which results in the simplified expression: 123x - 84y.

Step-by-step explanation:

The student made a mistake in the second step of solving an algebraic expression. The correct steps are as follows:

Multiply the terms in brackets: 12(8x - 4y) - 3(12y - 9x).

Distribute the multiplication over the terms in the brackets: 96x - 48y - 36y + 27x.

Combine like terms: (96x + 27x) - (48y + 36y).

Add the coefficients for like terms: (96 + 27)x - (48 + 36)y.

Simplify the expression: 123x - 84y.

Note that in step 2, when distributing the negative through the bracket we must change the sign of the terms inside. This common mistake leads to incorrect addition of coefficients in step 4.