Combine Like Terms 3

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Algebra 1

Algebraic Expressions

Combine Like Terms

Combine Like Terms 3

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Question 1 of 4

Simplify

$p^2+pq+3qp+q^2$

1. $pq^2+2pq$
2. $p^2+q^2+4pq$
3. $2p^2+4pq$
4. $p^2+q-4pq$

Question 2 of 4

2. Question
Simplify

$6n+5(3n+8)$
- (21n+40)
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When simplifying expressions, like terms can be combined or operated on.

Start by distributing $5$ so that we will have all terms separated.

$6n+5(3n+8)$

$=$ $6n+(5xx3n)+(5xx8)$

$=$ $6n+15n+40$

Since there are two terms that both have the variable $n$ , we can combine them.

$6$ $n$ $+15$ $n$ $+40$

$=$ $(6+15)$ $n$ $+40$ Solve the constants of like terms

$=$ $21n+40$

$21n+40$

Question 3 of 4

Simplify

$(x+3)-(x-y)$

(y+3)

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When simplifying expressions, like terms can be combined or operated on.

Start by distributing

$-1$ to the second parenthesis so that we will have all terms separated.

		$(x+3)-(x-y)$
	$=$	$x+3+[ (-1) \times x ]-[ (-1) \times y ]$
	$=$	$x+3-x+y$

Since there are two terms that both have the variable $x$ , we can combine them.

Note that variables without constants have

$1$ as a constant.

	$x$ $+3-$ $x$ $+y$
$=$	$(1-1)$ $x$ $+3+y$	Solve the constants of like terms
$=$	$(0)$ $x$ $+3+y$
$=$	$0+3+y$	$0$ multiplied to any number equals $0$
$=$	$y+3$	Rearrange the values further

$y+3$

Question 4 of 4

4. Question
Simplify

$4(x+2y)+3(5x-y)$
- (19x+5y)
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When simplifying expressions, like terms can be combined or operated on.

Start by distributing $4$ and $3$ to their respective parentheses so that we will have all terms separated.

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

$=$ $(4xx x)+(4xx2y)+(3xx5x)-(3xxy)$

$=$ $4x+8y+15x-3y$

Since there are two terms that both have the variable $x$ , we can combine them.

$4$ $x$ $+8y+15$ $x$ $-3y$

$=$ $(4+15)$ $x$ $+8y-3y$ Solve the constants of like terms

$=$ $19x+8y-3y$

There are also two terms that both have the variable $y$ , so we can combine them.

$19x+8$ $y$ $-3$ $y$

$=$ $19x+(8-3)$ $y$ Solve the constants of like terms

$=$ $19x+5y$

$19x+5y$

Combine Like Terms 3

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2. Question

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Quizzes

$=$	$p^2+$ $pq$ $+3qp+q^2$
	$p^2+$ $pq$ $+3$ $pq$ $+q^2$	$qp=pq$
$=$	$p^2+(1+3)$ $pq$ $+q^2$	Solve the constants of like terms
$=$	$p^2+q^2+4pq$	Rearrange the values further

	$6$ $n$ $+15$ $n$ $+40$
$=$	$(6+15)$ $n$ $+40$	Solve the constants of like terms
$=$	$21n+40$

		$4(x+2y)+3(5x-y)$
	$=$	$(4xx x)+(4xx2y)+(3xx5x)-(3xxy)$
	$=$	$4x+8y+15x-3y$

	$4$ $x$ $+8y+15$ $x$ $-3y$
$=$	$(4+15)$ $x$ $+8y-3y$	Solve the constants of like terms
$=$	$19x+8y-3y$

	$19x+8$ $y$ $-3$ $y$
$=$	$19x+(8-3)$ $y$	Solve the constants of like terms
$=$	$19x+5y$

		$6n+5(3n+8)$
	$=$	$6n+(5xx3n)+(5xx8)$
	$=$	$6n+15n+40$