Simplify: 4(2x + 3) − 2(x − 5)

Distribute each coefficient through its parentheses, watching signs. 4(2x + 3) = 8x + 12. −2(x − 5) = −2x + 10 (note: −2 times −5 = +10). Combine: 8x + 12 − 2x + 10. Combine like terms: (8x − 2x) + (12 + 10) = 6x + 22. The most common error is sign mistakes when distributing a negative coefficient — −2(x − 5) is −2·x + (−2)·(−5) = −2x + 10, NOT −2x − 10. Always distribute the sign with the coefficient. Like terms (terms with the same variable raised to the same power) can be combined; constants are like terms with each other; x terms are like terms with each other.