Question

match the model with the original expression containing parentheses and its simplified form. (there will be 6 piles with 3 cards in each pile.) 24x + 10 2(9x - 1) 4(6x + 2) 5(2x + 1) 10x - 16 8(3x + 2) 5(2x - 3) 24x + 8 3(6x - 3) 18x - 9 10x + 5 18x - 8

Explanation:

Step1: Use distributive property \(a(b + c)=ab+ac\)

For example, for \(5(2x - 3)\), we have \(5\times2x-5\times3 = 10x-15\).
For \(4(6x + 2)\), we get \(4\times6x+4\times2=24x + 8\).
For \(2(9x - 4)\), it is \(2\times9x-2\times4 = 18x-8\).
For \(8(3x + 2)\), we have \(8\times3x+8\times2=24x + 16\).
For \(3(6x - 3)\), we get \(3\times6x-3\times3=18x - 9\).
For \(5(2x + 1)\), it is \(5\times2x+5\times1 = 10x+5\).

Step2: Match with the given expressions

• For the rectangle with sides \(5\) and \((2x - 3)\), the expression is \(5(2x - 3)=10x - 15\) (not in the list).
• For the rectangle with sides \(4\) and \((6x + 2)\), the expression is \(4(6x + 2)=24x + 8\).
• For the rectangle with sides \(2\) and \((9x - 4)\), the expression is \(2(9x - 4)=18x - 8\).
• For the rectangle with sides \(8\) and \((3x + 2)\), the expression is \(8(3x + 2)=24x+16\) (not in the list).
• For the rectangle with sides \(3\) and \((6x - 3)\), the expression is \(3(6x - 3)=18x - 9\).
• For the rectangle with sides \(5\) and \((2x + 1)\), the expression is \(5(2x + 1)=10x + 5\).

Answer:

• Rectangle with sides \(4\) and \((6x + 2)\) matches with \(4(6x + 2)\) and \(24x + 8\).
• Rectangle with sides \(2\) and \((9x - 4)\) matches with \(2(9x - 4)\) and \(18x - 8\).
• Rectangle with sides \(3\) and \((6x - 3)\) matches with \(3(6x - 3)\) and \(18x - 9\).
• Rectangle with sides \(5\) and \((2x + 1)\) matches with \(5(2x + 1)\) and \(10x + 5\).