Question

Combine Like Terms:

A) 3b – 5 – 4b + 3
B) 3x + 6x + 5
C) – 2b – 6 + 9
D) 2a + 6 – 3b
E) 4x – 3 + 2y – y
F) 10x – 5y + 3x – 2

Answer 1

Combining like terms involves combining terms with the same variable and the same power, and constant numbers separately. The provided examples are simplified based on commutative and arithmetic properties, resulting in simplified expressions for each.

Step-by-step explanation:

Combining Like Terms

To combine like terms, we follow the mathematical principles of commutative property, which states A+B=B+A, and the rules for addition and multiplication of numbers with different signs. Let's simplify the expressions provided:

• A) 3b – 5 – 4b + 3: Combine like terms (terms with 'b' and the numbers). This gives us –b – 2 (since 3b – 4b = –b and –5 + 3 = –2).
• B) 3x + 6x + 5: Combine like terms (terms with 'x'). This gives us 9x + 5.
• C) –2b – 6 + 9: Combine the numbers. This gives us –2b + 3.
• D) 2a + 6 – 3b: There are no like terms with 'a' and 'b', so the expression remains the same.
• E) 4x – 3 + 2y – y: Combine like terms (terms with 'y'). This gives us 4x – 3 + y.
• F) 10x – 5y + 3x – 2: Combine like terms (terms with 'x' and then the numbers). This gives us 13x – 5y – 2.

Remember that when combining like terms, we only combine terms that have the exact same variable raised to the same power. After combining like terms, we also check if our simplification is reasonable.