Letters and like terms.

Step 1 of 5

A letter for a number

In the previous Unit we worked out expressions with numbers only. In algebra you write a letter, such as x, in place of a number: one you do not know yet, or any number at all. Such a letter is called a variable, because its value can vary.

A number written next to a letter hides a multiplication: $3x$⁠ means $3 \times x$⁠. On the board each x is a strip of length x, and each $1$⁠ is a square. $3x + 2$⁠ is three strips and two squares, and here $x = 4$⁠, so each strip is as long as four squares. Answer, then choose Sorted and worked out under Look inside to see the working under the board.

Step 2 of 5

A variable varies

The expression $3x + 2$⁠ does not fix one number: it has a different value for every value of x. Move x and notice: the strips grow and shrink, but there are always three strips and two squares. The value of the expression is written under the board.

Step 3 of 5

Like terms

An expression is made of terms that are added or subtracted: $2x + 3 + 4x + 1$⁠ has four terms. Like terms have the same letters: $2x$⁠ and $4x$⁠ are alike, and so are $3$⁠ and $1$⁠, which have no letter. Like terms can be collected into one term, just as you count strips with strips and squares with squares.

Each kind of term has its own colour on the board. Predict what is left after collecting, then watch the tiles sort themselves.

Step 4 of 5

Unlike terms

The y strip has length y, not x, so $3x$⁠ and $2y$⁠ are not like terms. Move x and y and notice that each kind of strip changes length on its own.

Step 5 of 5

A minus in front of a term

The sign in front of a term belongs to that term: in $5x + 4 - 2x - 1$⁠ the terms are $5x$⁠, $4$⁠, $-2x$⁠ and $-1$⁠. On the board a term with a minus is drawn pale, with an outline. A pale strip and a solid strip cancel each other, $x - x = 0$⁠, just as $5 + (-5) = 0$⁠ on the number line. Answer, then choose Sorted and worked out under Look inside and watch the pairs disappear.