Combine Like Terms 3

Topics

Pre - Algebra

Algebraic Expressions

Combine Like Terms

Combine Like Terms 3

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Question 1 of 4

Simplify

p^{2} + p q + 3 q p + q^{2}

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

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

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

The variable

q p

$qp$ can also be written as $p q$ $pq$ , and can be combined to another similar term.

Note that variables without constants have

1

$1$ as a constant.

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

p^{2} + q^{2} + 4 p q

$p^2+q^2+4pq$

Question 2 of 4

2. Question
Simplify

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

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

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

$=$ $=$ $6 n + (5 \times 3 n) + (5 \times 8)$ $6n+(5xx3n)+(5xx8)$

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

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

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

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

$=$ $=$ $21 n + 40$ $21n+40$

$21 n + 40$ $21n+40$

Question 3 of 4

Simplify

(x + 3) - (x - y)

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

(y+3)

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

Start by distributing

- 1

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

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

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

Note that variables without constants have

1

$1$ as a constant.

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

y + 3

$y+3$

Question 4 of 4

4. Question
Simplify

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

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

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

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

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

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

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

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

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

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

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

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

$=$ $=$ $19 x + 5 y$ $19x+5y$

$19 x + 5 y$ $19x+5y$

Combine Like Terms 3

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Quizzes

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

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

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

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

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