Question

mr. ramirez’s class was playing a game in which students need to match sticky notes that have equivalent expressions. how can you sort the expressions into groups? 10p - 8; 5p + 8 + 3p; 8p + 2p - 8; 10p + 4 + 2p + 2; 2(5p - 4); 8(p + 1); 4(2p + 2); 3p + 4p + 6 + 5p; 3(4p + 2)

Explanation:

Step1: Simplify each expression

• \(8p + 2p - 8\): Combine like terms \(8p+2p = 10p\), so \(10p - 8\).
• \(10p - 8\): Already simplified.
• \(2(5p - 4)\): Distribute 2: \(10p - 8\).
• \(5p + 8 + 3p\): Combine like terms \(5p+3p = 8p\), so \(8p + 8\).
• \(10p + 4 + 2p + 2\): Combine like terms \(10p+2p = 12p\), \(4 + 2 = 6\), so \(12p + 6\).
• \(8(p + 1)\): Distribute 8: \(8p + 8\).
• \(4(2p + 2)\): Distribute 4: \(8p + 8\).
• \(3p + 4p + 6 + 5p\): Combine like terms \(3p+4p+5p = 12p\), so \(12p + 6\).
• \(3(4p + 2)\): Distribute 3: \(12p + 6\).

Step2: Group equivalent expressions

• Group 1 (\(10p - 8\)): \(8p + 2p - 8\), \(10p - 8\), \(2(5p - 4)\)
• Group 2 (\(8p + 8\)): \(5p + 8 + 3p\), \(8(p + 1)\), \(4(2p + 2)\)
• Group 3 (\(12p + 6\)): \(10p + 4 + 2p + 2\), \(3p + 4p + 6 + 5p\), \(3(4p + 2)\)

Answer:

• Group 1 (Equivalent to \(10p - 8\)): \(8p + 2p - 8\), \(10p - 8\), \(2(5p - 4)\)
• Group 2 (Equivalent to \(8p + 8\)): \(5p + 8 + 3p\), \(8(p + 1)\), \(4(2p + 2)\)
• Group 3 (Equivalent to \(12p + 6\)): \(10p + 4 + 2p + 2\), \(3p + 4p + 6 + 5p\), \(3(4p + 2)\)