Algebraic Expressions
Name: ______________________
Date: _______________________
Parts of an algebraic expression are called _________________. _____________ ______________ are
terms that have the same ________________ raised to the same exponents. __________________ terms
are also like terms.
Identify the terms and ______________ terms in each ________________________.
{
-x
Terms:
𝑧 2 , 5z
−3𝑧 2 ,
{
{
7,
{
{
-2,
{
{
Terms: 9x,
{
b. 𝑧 2 + 5z - 3𝑧 2 + 𝑧
Rewrite as a sum of terms.
𝑧 2 + 5z + (−3𝑧 2 ) + 𝑧
a. 9x – 2 + 7 – x
Rewrite as a sum of terms.
9x + (-2) + 7 + (-x)
z
Like Terms: 𝑧 2 and −3𝑧 2
5z and z
Like Terms: 9x and –x
-2 and 7
On Your Own
Identify the terms and like terms in each expression.
1. y + 10 –
3
2
2. 2𝑟 2 + 7𝑟 − 𝑟 2 − 9
𝑦
Terms: _____ _______ ________
Terms: ________ ________ _______ _______
Like Terms: ______ and _______
_________
Like Terms: _________ and _________
_________
__________
An algebraic expression is in ____________ __________ when it has no like terms and no parentheses.
𝟑
𝟏
Simplify 𝟒 𝒚 + 𝟏𝟐 − 𝟐 𝒚 − 𝟔
𝟑
𝟒
𝟏
𝟑
𝟏
𝒚 + 𝟏𝟐 − 𝟐 𝒚 − 𝟔 = 𝟒 𝒚 + 𝟏𝟐 + (− 𝟐 𝒚) + (−𝟔)
𝟑
𝟏
= 𝟒 𝒚 + (− 𝟐 𝒚) + 𝟏𝟐 + (−𝟔)
𝟑
𝟏
= [𝟒 + (− 𝟐)] 𝒚 + 𝟏𝟐 + (−𝟔)
𝟏
= 𝟒𝒚 + 𝟔
Rewrite as a sum
Commutative Property of Addition
Distributive Property
Combine Like Terms
Algebraic Expressions
Name: ______________________
Date: _______________________
Do It together
Simplify the expression.
𝟖𝒔 − 𝟏𝟏𝒔 + 𝟔
Rewrite as a sum.
Distributive Property
Combine Like Terms
On Your Own
Simplify each expression.
3. 14 − 3𝑧 + 8 + 𝑧
4. 2.5𝑥 + 4.3𝑥 − 5
5.
3
8
3
𝑏 − 4𝑏
Simplifying an Algebraic Expression using The ________________ Property.
𝟏
Simplify − 𝟐 (𝟔𝒏 + 𝟒) + 𝟐𝒏.
1
1
1
− 2 (6𝑛 + 4) + 2𝑛 = − 2 (6𝑛) + (− 2) (4) + 2𝑛
= -3n + (-2) + 2n
= -3n + 2n + (-2)
= (-3 + 2)n + (-2)
= -n – 2
Distributive Property
Multiply.
Commutative Property of Addition
Distributive Property
Simplify.
Do It together
Simplify the expression.
3(q + 1) - 4
__________________________________________
Distributive Property
__________________________________________
Multiply.
__________________________________________
Simplify.
Algebraic Expressions
On Your Own
Simplify each expression.
6. -2(g + 4) + 7g
Name: ______________________
Date: _______________________
3
1
7. 7 − 4(4 𝑥 − 4)
Algebraic Expressions
Name: ______________________
Date: _______________________
Parts of an algebraic expression are called terms. Like terms are terms that have the same variables
raised to the same exponents. Constant terms are also like terms.
Identify the terms and like terms in each expression.
{
-x
Terms:
𝑧 2 , 5z
−3𝑧 2 ,
{
{
7,
{
{
-2,
{
{
Terms: 9x,
{
b. 𝑧 2 + 5z - 3𝑧 2 + 𝑧
Rewrite as a sum of terms.
𝑧 2 + 5z + (−3𝑧 2 ) + 𝑧
a. 9x – 2 + 7 – x
Rewrite as a sum of terms.
9x + (-2) + 7 + (-x)
z
Like Terms: 𝑧 2 and −3𝑧 2
5z and z
Like Terms: 9x and –x
-2 and 7
On Your Own
Identify the terms and like terms in each expression.
1. y + 10 –
3
2
2. 2𝑟 2 + 7𝑟 − 𝑟 2 − 9
𝑦
–
Terms: y 10
𝟑
Terms: 𝟐𝒓𝟐 7r −𝒓𝟐
𝒚
𝟐
𝟑
−𝟗
Like Terms: 𝟐𝒓𝟐 and −𝒓𝟐
Like Terms: y and – 𝟐 𝒚
10
7r
−𝟗
An algebraic expression is in simplest form when it has no like terms and no parentheses.
𝟑
𝟏
Simplify 𝟒 𝒚 + 𝟏𝟐 − 𝟐 𝒚 − 𝟔
𝟑
𝟒
𝟏
𝟑
𝟏
𝒚 + 𝟏𝟐 − 𝟐 𝒚 − 𝟔 = 𝟒 𝒚 + 𝟏𝟐 + (− 𝟐 𝒚) + (−𝟔)
𝟑
𝟏
= 𝟒 𝒚 + (− 𝟐 𝒚) + 𝟏𝟐 + (−𝟔)
𝟑
𝟏
= [𝟒 + (− 𝟐)] 𝒚 + 𝟏𝟐 + (−𝟔)
𝟏
= 𝟒𝒚 + 𝟔
Rewrite as a sum
Commutative Property of Addition
Distributive Property
Combine Like Terms
Algebraic Expressions
Name: ______________________
Date: _______________________
Do It together
Simplify the expression.
𝟖𝒔 − 𝟏𝟏𝒔 + 𝟔
8s + (-11s) + 6
Rewrite as a sum.
[(𝟖 + (−𝟏𝟏)]𝒔 + 𝟔
Distributive Property
-3s + 6
Combine Like Terms
On Your Own
Simplify each expression.
3. 14 − 3𝑧 + 8 + 𝑧
4. 2.5𝑥 + 4.3𝑥 − 5
14 + (-3z) + 8 + z
2.5x + 4.3x + (-5)
(-3z) + z + 14 + 8
6.8x – 5
3
5.
𝟑
8
3
𝑏 − 4𝑏
𝟑
𝒃 + (− 𝟒 𝒃)
𝟖
𝟑
𝟖
𝟔
𝒃 + (− 𝟖 𝒃)
𝟑
−𝟖𝒃
-2z + 22
Simplifying an Algebraic Expression using The ________________ Property.
𝟏
Simplify − 𝟐 (𝟔𝒏 + 𝟒) + 𝟐𝒏.
1
1
1
− 2 (6𝑛 + 4) + 2𝑛 = − 2 (6𝑛) + (− 2) (4) + 2𝑛
= -3n + (-2) + 2n
= -3n + 2n + (-2)
= (-3 + 2)n + (-2)
= -n – 2
Distributive Property
Multiply.
Commutative Property of Addition
Distributive Property
Simplify.
Do It together
Simplify the expression.
3(q + 1) - 4
3(q + 1) – 4 = 3(q) + 3(1) + (-4)
Distributive Property
= 3q + 3 + (-4)
Multiply.
= 3q -1
Simplify.
Algebraic Expressions
On Your Own
Simplify each expression.
6. -2(g + 4) + 7g
Name: ______________________
Date: _______________________
3
1
7. 7 − 4(4 𝑥 − 4)
𝟑
𝟏
-2(g) + (-2)(4) + 7g
𝟕 + (−𝟒) (𝟒 𝒙) + (−𝟒)(− 𝟒)
-2g + (-8) + 7g
7 + (–3x) + 1
-2g + 7g + (-8)
7 + 1 + (-3x)
5g – 8
8 – 3x