Arithmetic with Expressions: Practice

Like terms with the same variable part combine by adding their coefficients.

$3x + 5x = (3 + 5)x = 8x$

The variable part stays $x$; it does not become $x^2$.

Like terms have the same variable part.

$3x \text{ and } 7x$

Both have variable part $x$. The other pairs differ in letter, exponent, or having a variable at all.

The constant term is the term with no variable.

$4x + 7 \rightarrow 7$

Drop the parentheses and combine like terms.

$(2x + 3) + (5x + 1) = 7x + 4$

Multiply the $2$ across both terms inside.

$2(x + 3) = 2x + 6$

The lone $a$ has coefficient $1$.

$7a - a = (7 - 1)a = 6a$

Group the $x$ terms and the constants.

$3x + 2 + x + 5 = (3x + x) + (2 + 5) = 4x + 7$

Combine like terms across the two groups.

$(4x + 5) + (3x + 2) = 7x + 7$

Only $2a$ and $4a$ are like terms; $3b$ has a different variable part.

$2a + 3b + 4a = 6a + 3b$

A variable written alone carries an invisible coefficient of $1$.

$y = 1y$

Add and subtract the coefficients, counting the lone $x$ as $1$.

$6x - 2x + x = (6 - 2 + 1)x = 5x$

Combine like terms first, then substitute $x = 4$.

$2x + 3x = 5x, \quad 5(4) = 20$