Combining Like Terms 2

Years

Year 10

Algebraic Expressions

Combining Like Terms

Combining Like Terms 2

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Question 1 of 4

1. Question
Simplify

$7 x + 6 y^{2} - 3 + y^{2} - 5 x$ $7x+6y^2-3+y^2-5x$
- 1. $7 y^{2} + 2 x - 3$ $7y^2+2x-3$
- 2. $6 y^{2} - 12 x + 3$ $6y^2-12x+3$
- 3. $- 15 x^{2} - 9 y$ $-15x^2-9y$
- 4. $6 y^{2} + 12 x - 3$ $6y^2+12x-3$
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When simplifying expressions, like terms can be combined or operated on.

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

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

$7 x + 6$ $7x+6$ $y^{2}$ $y^2$ $- 3 +$ $-3+$ $y^{2}$ $y^2$ $- 5 x$ $-5x$

$=$ $=$ $(6 + 1)$ $(6+1)$ $y^{2}$ $y^2$ $+ 7 x - 3 - 5 x$ $+7x-3-5x$ Solve the constants of like terms

$=$ $=$ $7 y^{2} + 7 x - 3 - 5 x$ $7y^2+7x-3-5x$

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

$7 y^{2} + 7$ $7y^2+7$ $x$ $x$ $- 3 - 5$ $-3-5$ $x$ $x$

$=$ $=$ $7 y^{2} + (7 - 5)$ $7y^2+(7-5)$ $x$ $x$ $- 3$ $-3$ Solve the constants of like terms

$=$ $=$ $7 y^{2} + 2 x - 3$ $7y^2+2x-3$

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

Question 2 of 4

Simplify

3 b^{2} - 9 + 2 b - b^{2} + 4 b - 2 a

$3b^2-9+2b-b^2+4b-2a$

1. $2 b^{2} + 6 b - 2 a - 9$ $2b^2+6b-2a-9$
2. $2 b^{2} + 8 a b - 9$ $2b^2+8ab-9$
3. $4 b^{2} - 6 b - 11 a$ $4b^2-6b-11a$
4. $4 b^{2} + 4 b + 2 a - 9$ $4b^2+4b+2a-9$

Question 3 of 4

Simplify

7 a b + 4 b c - 3 a b - c b

$7ab+4bc-3ab-cb$

(4ab+3bc)

Question 4 of 4

Simplify

9 a^{2} + 3 a b + 2 b a + 4 a^{2}

$9a^2+3ab+2ba+4a^2$

1. $13 a^{2} + 5 a b$ $13a^2+5ab$
2. $13 a^{2} - a b$ $13a^2-ab$
3. $5 a^{2} - 5 a b$ $5a^2-5ab$
4. $5 a^{2} + a b$ $5a^2+ab$

$=$ $=$	$4 a b + 4$ $4ab+4$ $b c$ $bc$ $- c b$ $-cb$
	$4 a b + 4$ $4ab+4$ $b c$ $bc$ $-$ $-$ $b c$ $bc$	$c b = b c$ $cb=bc$
$=$ $=$	$4 a b + (4 - 1)$ $4ab+(4-1)$ $b c$ $bc$	Solve the constants of like terms
$=$ $=$	$4 a b + 3 b c$ $4ab+3bc$

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Quizzes

	$7 x + 6$ $7x+6$ $y^{2}$ $y^2$ $- 3 +$ $-3+$ $y^{2}$ $y^2$ $- 5 x$ $-5x$
$=$ $=$	$(6 + 1)$ $(6+1)$ $y^{2}$ $y^2$ $+ 7 x - 3 - 5 x$ $+7x-3-5x$	Solve the constants of like terms
$=$ $=$	$7 y^{2} + 7 x - 3 - 5 x$ $7y^2+7x-3-5x$

	$7 y^{2} + 7$ $7y^2+7$ $x$ $x$ $- 3 - 5$ $-3-5$ $x$ $x$
$=$ $=$	$7 y^{2} + (7 - 5)$ $7y^2+(7-5)$ $x$ $x$ $- 3$ $-3$	Solve the constants of like terms
$=$ $=$	$7 y^{2} + 2 x - 3$ $7y^2+2x-3$

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

	$2 b^{2} - 9 + 2$ $2b^2-9+2$ $b$ $b$ $+ 4$ $+4$ $b$ $b$ $- 2 a$ $-2a$
$=$ $=$	$2 b^{2} - 9 + (2 + 4)$ $2b^2-9+(2+4)$ $b$ $b$ $- 2 a$ $-2a$	Solve the constants of like terms
$=$ $=$	$2 b^{2} + 6 b - 2 a - 9$ $2b^2+6b-2a-9$	Rearrange the values further

	$7$ $7$ $a b$ $ab$ $+ 4 b c - 3$ $+4bc-3$ $a b$ $ab$ $- c b$ $-cb$
$=$ $=$	$(7 - 3)$ $(7-3)$ $a b$ $ab$ $+ 4 b c - c b$ $+4bc-cb$	Solve the constants of like terms
$=$ $=$	$4 a b + 4 b c - c b$ $4ab+4bc-cb$

	$9$ $9$ $a^{2}$ $a^2$ $+ 3 a b + 2 b a + 4$ $+3ab+2ba+4$ $a^{2}$ $a^2$
$=$ $=$	$(9 + 4)$ $(9+4)$ $a^{2}$ $a^2$ $+ 3 a b + 2 b a$ $+3ab+2ba$	Solve the constants of like terms
$=$ $=$	$13 a^{2} + 3 a b + 2 b a$ $13a^2+3ab+2ba$

$=$ $=$	$13 a^{2} + 3$ $13a^2+3$ $a b$ $ab$ $+ 2 b a$ $+2ba$
	$13 a^{2} + 3$ $13a^2+3$ $a b$ $ab$ $+ 2$ $+2$ $a b$ $ab$	$b a = a b$ $ba=ab$
$=$ $=$	$13 a^{2} + (3 + 2)$ $13a^2+(3+2)$ $a b$ $ab$	Solve the constants of like terms
$=$ $=$	$13 a^{2} + 5 a b$ $13a^2+5ab$