Combining Like Terms 1

Years

Year 10

Algebraic Expressions

Combining Like Terms

Combining Like Terms 1

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Question 1 of 4

1. Question
Simplify

$9 x + 3 x - 5 x$ $9x+3x-5x$
- (7x)
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When simplifying expressions, like terms can be combined or operated on.

Since all the terms in the expression have the variable $x$ $x$ , they are all like terms.

This means we can directly add and subtract them.

$9$ $9$ $x$ $x$ $+ 3$ $+3$ $x$ $x$ $- 5$ $-5$ $x$ $x$

$=$ $=$ $(9 + 3 - 5)$ $(9+3-5)$ $x$ $x$ Solve the constants

$=$ $=$ $7 x$ $7x$

$7 x$ $7x$
Question 2 of 4

2. Question
Simplify

$2 f - 6 y + 3 f$ $2f-6y+3f$
- (5f-6y)
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When simplifying expressions, like terms can be combined or operated on.

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

$2$ $2$ $f$ $f$ $- 6 y + 3$ $-6y+3$ $f$ $f$

$=$ $=$ $(2 + 3)$ $(2+3)$ $f$ $f$ $- 6 y$ $-6y$ Solve the constants of like terms

$=$ $=$ $5 f - 6 y$ $5f-6y$

$5 f - 6 y$ $5f-6y$
Question 3 of 4

3. Question
Simplify

$7 x^{2} + 3 x - 4 x^{2} - x$ $7x^2+3x-4x^2-x$
- 1. $3 x^{2} + 2 x$ $3x^2+2x$
- 2. $11 x^{2} + 4 x$ $11x^2+4x$
- 3. $7 x^{2} - 4 x$ $7x^2-4x$
- 4. $11 x^{2} - 2 x$ $11x^2-2x$
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When simplifying expressions, like terms can be combined or operated on.

There are two terms that both have the variable $x^{2}$ $x^2$ , so we can combine them.

$7$ $7$ $x^{2}$ $x^2$ $+ 3 x - 4$ $+3x-4$ $x^{2}$ $x^2$ $- x$ $-x$

$=$ $=$ $(7 - 4)$ $(7-4)$ $x^{2}$ $x^2$ $+ 3 x - x$ $+3x-x$ Solve the constants of like terms

$=$ $=$ $3 x^{2} + 3 x - x$ $3x^2+3x-x$

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

Note that variables without constants have $1$ $1$ as a constants.

$3 x^{2} + 3$ $3x^2+3$ $x$ $x$ $-$ $-$ $x$ $x$

$=$ $=$ $3 x^{2} + (3 - 1)$ $3x^2+(3-1)$ $x$ $x$ Solve the constants of like terms

$=$ $=$ $3 x^{2} + 2 x$ $3x^2+2x$

$3 x^{2} + 2 x$ $3x^2+2x$
Question 4 of 4

4. Question
Simplify

$3 m^{2} + 4 - 2 m + m^{2} + 9$ $3m^2+4-2m+m^2+9$
- 1. $4 m^{2} - 2 m + 13$ $4m^2-2m+13$
- 2. $4 m^{2} - 2 m + 5$ $4m^2-2m+5$
- 3. $6 m^{2} + 13$ $6m^2+13$
- 4. $2 m^{2} - 2 m - 5$ $2m^2-2m-5$
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When simplifying expressions, like terms can be combined or operated on.

There are two terms that both have the variable $m^{2}$ $m^2$ , so we can combine them.

Note that variables without constants have $1$ $1$ as a constant.

$3$ $3$ $m^{2}$ $m^2$ $+ 4 - 2 m +$ $+4-2m+$ $m^{2}$ $m^2$ $+ 9$ $+9$

$=$ $=$ $(3 - 1)$ $(3-1)$ $m^{2}$ $m^2$ $+ 4 - 2 m + 9$ $+4-2m+9$ Solve the constants of like terms

$=$ $=$ $4 m^{2} + 4 - 2 m + 9$ $4m^2+4-2m+9$

There are also two terms that have no variables, so we can combine them.

$4 m^{2} +$ $4m^2+$ $4$ $4$ $- 2 m +$ $-2m+$ $9$ $9$

$=$ $=$ $4 m^{2} - 2 m +$ $4m^2-2m+$ $(4 + 9)$ $(4+9)$ Solve the constants of like terms

$=$ $=$ $4 m^{2} - 2 m + 13$ $4m^2-2m+13$

$4 m^{2} - 2 m + 13$ $4m^2-2m+13$

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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Quizzes

	$9$ $9$ $x$ $x$ $+ 3$ $+3$ $x$ $x$ $- 5$ $-5$ $x$ $x$
$=$ $=$	$(9 + 3 - 5)$ $(9+3-5)$ $x$ $x$	Solve the constants
$=$ $=$	$7 x$ $7x$

	$2$ $2$ $f$ $f$ $- 6 y + 3$ $-6y+3$ $f$ $f$
$=$ $=$	$(2 + 3)$ $(2+3)$ $f$ $f$ $- 6 y$ $-6y$	Solve the constants of like terms
$=$ $=$	$5 f - 6 y$ $5f-6y$

	$7$ $7$ $x^{2}$ $x^2$ $+ 3 x - 4$ $+3x-4$ $x^{2}$ $x^2$ $- x$ $-x$
$=$ $=$	$(7 - 4)$ $(7-4)$ $x^{2}$ $x^2$ $+ 3 x - x$ $+3x-x$	Solve the constants of like terms
$=$ $=$	$3 x^{2} + 3 x - x$ $3x^2+3x-x$

	$3 x^{2} + 3$ $3x^2+3$ $x$ $x$ $-$ $-$ $x$ $x$
$=$ $=$	$3 x^{2} + (3 - 1)$ $3x^2+(3-1)$ $x$ $x$	Solve the constants of like terms
$=$ $=$	$3 x^{2} + 2 x$ $3x^2+2x$

	$3$ $3$ $m^{2}$ $m^2$ $+ 4 - 2 m +$ $+4-2m+$ $m^{2}$ $m^2$ $+ 9$ $+9$
$=$ $=$	$(3 - 1)$ $(3-1)$ $m^{2}$ $m^2$ $+ 4 - 2 m + 9$ $+4-2m+9$	Solve the constants of like terms
$=$ $=$	$4 m^{2} + 4 - 2 m + 9$ $4m^2+4-2m+9$

	$4 m^{2} +$ $4m^2+$ $4$ $4$ $- 2 m +$ $-2m+$ $9$ $9$
$=$ $=$	$4 m^{2} - 2 m +$ $4m^2-2m+$ $(4 + 9)$ $(4+9)$	Solve the constants of like terms
$=$ $=$	$4 m^{2} - 2 m + 13$ $4m^2-2m+13$