5 Expand and simplify each expression. a \( a(a+3)+a(a+4) \) b \( b(b+3)+b(4 b+5) \) c \( c(3 c+4)+c(5 c+6) \) d \( d(3 d+4)-d(d+5) \) e \( e(3+4 e)-e(5 e-6) \) f \( f(3 f+4 g)-5 f(6 f-7 g) \)

Let's expand and simplify each expression step by step! a: \( a(a+3) + a(a+4) \) = \( a^2 + 3a + a^2 + 4a \) = \( 2a^2 + 7a \) b: \( b(b+3) + b(4b+5) \) = \( b^2 + 3b + 4b^2 + 5b \) = \( 5b^2 + 8b \) c: \( c(3c+4) + c(5c+6) \) = \( 3c^2 + 4c + 5c^2 + 6c \) = \( 8c^2 + 10c \) d: \( d(3d+4) - d(d+5) \) = \( 3d^2 + 4d - (d^2 + 5d) \) = \( 3d^2 + 4d - d^2 - 5d \) = \( 2d^2 - d \) e: \( e(3+4e) - e(5e-6) \) = \( 3e + 4e^2 - (5e^2 - 6e) \) = \( 3e + 4e^2 - 5e^2 + 6e \) = \( -e^2 + 9e \) f: \( f(3f+4g) - 5f(6f-7g) \) = \( 3f^2 + 4fg - (30f^2 - 35fg) \) = \( 3f^2 + 4fg - 30f^2 + 35fg \) = \( -27f^2 + 39fg \) These are your expanded and simplified forms! Happy math exploring!