To determine which phrase matches the expression [tex]\( c^3 \)[/tex], let's analyze each option:
A. [tex]$c$[/tex] increased by 3: This phrase corresponds to the arithmetic operation of adding 3 to [tex]\( c \)[/tex]. Mathematically, it can be written as [tex]\( c + 3 \)[/tex]. This does not match [tex]\( c^3 \)[/tex].
B. the sum of 3 and [tex]$c$[/tex]: This phrase also corresponds to the arithmetic operation of adding [tex]\( c \)[/tex] and 3. Mathematically, it can be written as [tex]\( 3 + c \)[/tex]. This does not match [tex]\( c^3 \)[/tex].
C. 3 cubed: This phrase describes the number 3 raised to the power of 3, written as [tex]\( 3^3 \)[/tex], which equals 27. This does not match [tex]\( c^3 \)[/tex].
D. c cubed: This phrase describes [tex]\( c \)[/tex] raised to the power of 3, written as [tex]\( c^3 \)[/tex]. This matches the given expression exactly.
Therefore, the correct phrase that matches the expression [tex]\( c^3 \)[/tex] is:
D. c cubed
