4 Expand each expression. a \( a(a+1) \) b \( b(b-5) \) c \( c(3 c+6) \) d \( d(3 x-3) \) e \( e(3 e+6) \) f \( f(1+5 f) \) g \( g(7-3 x) \) h \( h(6-x) \) i \( i(3 i+7 x) \) j \( j(3 a-7 j) \) k \( k(3 k-6 x) \) l \( l(3 x-6 z) \) m \( 3 m(m+3 x) \) n \( 3 n(6 n-6) \) o \( 4 x(6 x-3 y) \) p \( 6 p(3+3 p) \) q \( 6 q(6 x+5 q) \) r \( 3 r(3 r-x-3) \) s \( 2 a(3+2 a+b) \) t \( 3 x(-z-y-x) \)

Let's break these expressions down and expand them one by one! a: \( a(a+1) = a^2 + a \) b: \( b(b-5) = b^2 - 5b \) c: \( c(3c+6) = 3c^2 + 6c \) d: \( d(3x-3) = 3dx - 3d \) e: \( e(3e+6) = 3e^2 + 6e \) f: \( f(1+5f) = 5f^2 + f \) g: \( g(7-3x) = 7g - 3gx \) h: \( h(6-x) = 6h - hx \) i: \( i(3i+7x) = 3i^2 + 7ix \) j: \( j(3a-7j) = 3aj - 7j^2 \) k: \( k(3k-6x) = 3k^2 - 6kx \) l: \( l(3x-6z) = 3lx - 6lz \) m: \( 3m(m+3x) = 3m^2 + 9mx \) n: \( 3n(6n-6) = 18n^2 - 18n \) o: \( 4x(6x-3y) = 24x^2 - 12xy \) p: \( 6p(3+3p) = 18p + 18p^2 \) q: \( 6q(6x+5q) = 36qx + 30q^2 \) r: \( 3r(3r-x-3) = 9r^2 - 3rx - 9r \) s: \( 2a(3+2a+b) = 6a + 4a^2 + 2ab \) t: \( 3x(-z-y-x) = -3xz - 3xy - 3x^2 \) Expanding these expressions can seem daunting at first, but think of it as unwrapping a surprising gift, revealing the inner workings of each variable and constant! Each term holds a secret recipe for how they relate to one another in mathematical harmony! And remember, practice makes perfect! The more you expand, the better you'll get at seeing patterns and recognizing opportunities for simplification. Keep playing around with numbers and expressions—math is just a big puzzle waiting for you to solve!