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Equivalent expressions and like terms
Equivalent algebraic expressions, identifying like terms, and simplifying expressions by adding and subtracting like terms.
Equivalent expressions
Two expressions are equivalent if they give the same value for every value of the pronumerals. $2x + x$ and $3x$ are equivalent. $x + 2$ and $2x$ are not: try $x = 5$.
Like terms
Simplify $5a + 3b - 2a + b$.
$a$ terms: $5a - 2a = 3a$. $b$ terms: $3b + b = 4b$.
$= 3a + 4b$
Simplify $4xy - 3x + 2yx + 7 - x$.
$4xy + 2xy = 6xy$, $\;-3x - x = -4x$
$= 6xy - 4x + 7$
Like terms
Same pronumeral part, e.g. $5xy$ and $-yx$.
$7m - m$
$6m$
Can $2x + 3y$ be simplified?
No.
Simplify $5a + 3b - 2a + b$.
Collect $a$ and $b$ terms.
Simplify $4xy - 3x + 2yx + 7 - x$.
$xy = yx$.
Simplify $7m - m$.
$7m - 1m$.
Which pair are like terms?
$pq = qp$.
Which is equivalent to $2x + 3 + x$?
$2x + x = 3x$.
Simplify $4k - 4k$.
They cancel.
Simplify $3a^2 + 2a - a^2 - a$.
$2a^2 + a$.
$x + 2$ and $2x$ are:
At $x = 5$: $7 \ne 10$.
New numbers every time. Keep going until you get five in a row.