Expand the following: a) \( 2(x+3) \) b) \( 5(2 x-4) \) c) \( 4(2 x+1) \) d) \( 6(x-4 y) \)

When you expand these expressions, you're essentially distributing the number outside the parentheses to every term inside: a) \( 2(x+3) = 2x + 6 \) You're simply taking the 2 and multiplying it by both \( x \) and 3, resulting in \( 2x \) and \( 6 \). b) \( 5(2 x-4) = 10x - 20 \) Here, multiply 5 by \( 2x \) to get \( 10x \) and 5 by -4 to get -20. c) \( 4(2 x+1) = 8x + 4 \) Distributing the 4, you multiply it by \( 2x \) to get \( 8x \) and by 1 to get 4. d) \( 6(x-4 y) = 6x - 24y \) Multiplying 6 by \( x \) gives you \( 6x \) and 6 by -4y gives you -24y. There you have it—each expression expanded beautifully!