4.3Addition and Subtraction of Linear Expressions

Think of $x$ as an object, like apples: $3x + 5x = 8x$ the way three apples and five make eight. Like terms share the same variables raised to the same powers, and only like terms combine.

$2x$ and $5x$ are like terms (same variable $x$ )
$7$ and $-4$ are like terms (both constants)
$-3xy$ and $2yx$ are like terms (since $xy = yx$ )
$2x$ and $3y$ are unlike terms (different variables)
$2x$ and $x^2$ are unlike terms (different powers)

Combining like terms

\displaystyle ax + bx = (a + b)x

Now you try

Simplify $9x - 4x$ .

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\displaystyle 9x - 4x

\displaystyle = (9 - 4)x

\displaystyle = 5x

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Simplifying by combining like terms

Simplify $\displaystyle 7a - 3b + 2a + 5b - a$ .

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Group like terms:

(7a + 2a - a) + (-3b + 5b)

= 8a + 2b

Subtracting an expression

Subtract $\displaystyle (4m + 9)$ from $\displaystyle (10m - 1)$ .

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"Subtract

A

from

B

" means

B - A

(10m - 1) - (4m + 9)

= 10m - 1 - 4m - 9 \quad \scriptsize\textit{distribute the negative}

= 6m - 10

Now you try

Simplify $4x + 5y - 2x - 3y$ .

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Group like terms:

(4x - 2x) + (5y - 3y)

= 2x+2y

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