Identify Equivalent Expressions

How the lesson starts: Identify Equivalent Expressions

Detective Ollie
Hello, detective! Ollie the owl solves math mysteries. Today's case: are x + x + x and 3x the same? They look different, like one wearing a disguise. Two expressions are equivalent if they give the same value for every number. Let's investigate!
Test some numbers
Ollie tests clues. Try x = 1, x = 2, and x = 5. x + x + x gives 3, 6 and 15. 3x gives 3, 6 and 15. A perfect match every time! But x³ gives 1, 8 and 125. No match. So x + x + x is equivalent to 3x, not x³.
Let's match twins
Ollie matches twins. 2(a + 5) means 2 × a plus 2 × 5, so its twin is 2a + 10. And a + a is just 2a. Going backwards, 3a + 12 is 3 × a plus 3 × 4, so its twin is 3(a + 4). Same value, new disguise!