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Core Knowledge

Like terms can be collected together by adding or subtracting their coefficients. Terms are like when they have exactly the same variable parts (same letters with same powers). When terms are not like, we cannot collect them. This process of collecting like terms is also called simplifying.

Example

Can the following be simplified? Answer yes or no.
a) $$4x^2 + 3 =$$ $$\text{No}$$
b) $$4x^2 + 3x^2 =$$ $$\text{Yes}$$

Example

Can the following be simplified? Answer yes or no.
c) $$4x + 3y =$$
d) $$4a + 3a =$$
e) $$12a + 7a^2 =$$
f) $$\dfrac{1}{2}a + \dfrac{1}{2}a =$$
g) $$\dfrac{1}{2}a + \dfrac{3}{4}a =$$
h) $$\dfrac{1}{2}b + \dfrac{3}{4}c^2 =$$

Question 1

On your whiteboards, can the following be simplified? Answer yes or no.
a)$$5x + 2x =$$
b)$$3y^2 + 4y^2 =$$
c)$$7m + 2n =$$
d)$$9p^2 + 3p =$$

Answers

Show me your whiteboards.
a)
$$5x + 2x =$$ $$\text{Yes}$$
b)
$$3y^2 + 4y^2 =$$ $$\text{Yes}$$
c)
$$7m + 2n =$$ $$\text{No}$$
d)
$$9p^2 + 3p =$$ $$\text{No}$$

Question 2

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, can the following be simplified? Answer yes or no.
a)$$4c - 2c =$$
b)$$4a^2b^2 - 2a^2b^3 =$$
c)$$6x^3y^2 - 3x^3y^2 =$$
d)$$5m^2n - 2mn^2 =$$

Answers

Show me your whiteboards.
a)
$$4c - 2c =$$ $$\text{Yes}$$
b)
$$4a^2b^2 - 2a^2b^3 =$$ $$\text{No}$$
c)
$$6x^3y^2 - 3x^3y^2 =$$ $$\text{Yes}$$
d)
$$5m^2n - 2mn^2 =$$ $$\text{No}$$

Core Knowledge

When we collect like terms, we add or subtract their coefficients and keep the variable part unchanged. For example, $3x^2 + 4x^2 = 7x^2$.

Example

Simplify the following:
a) $$3x^2 + 2x^2 =$$ $$5x^2$$
b) $$5ab + 3ab =$$ $$8ab$$

Example

Simplify the following:
c) $$4y^2 + 6y^2 =$$
d) $$7mn + 2mn =$$

Question 3

On your whiteboards, simplify the following:
a)$$6a^2 + 3a^2 =$$
b)$$8pq + 5pq =$$
c)$$9x^2 + 4x^2 =$$
d)$$2cd + 7cd =$$

Answers

Show me your whiteboards.
a)
$$6a^2 + 3a^2 =$$ $$9a^2$$
b)
$$8pq + 5pq =$$ $$13pq$$
c)
$$9x^2 + 4x^2 =$$ $$13x^2$$
d)
$$2cd + 7cd =$$ $$9cd$$

Question 4

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, simplify the following:
a)$$3a^2 + a^2 =$$
b)$$x^2 + x^2 =$$
c)$$ax^2 + ax^2 =$$
d)$$5m^3 + m^3 =$$

Answers

Show me your whiteboards.
a)
$$3a^2 + a^2 =$$ $$4a^2$$
b)
$$x^2 + x^2 =$$ $$2x^2$$
c)
$$ax^2 + ax^2 =$$ $$2ax^2$$
d)
$$5m^3 + m^3 =$$ $$6m^3$$

Core Knowledge

When subtracting like terms, subtract the coefficients. The result might be a negative coefficient.

Example

Simplify the following:
a) $$3x^2 - 8x^2 =$$ $$-5x^2$$
b) $$4ab - 9ab =$$ $$-5ab$$

Example

Simplify the following:
c) $$2y^2 - 7y^2 =$$
d) $$6mn - 11mn =$$

Question 5

On your whiteboards, simplify the following:
a)$$4a^2 - 10a^2 =$$
b)$$7pq - 12pq =$$
c)$$9x^2 - 15x^2 =$$
d)$$5cd - 13cd =$$

Answers

Show me your whiteboards.
a)
$$4a^2 - 10a^2 =$$ $$-6a^2$$
b)
$$7pq - 12pq =$$ $$-5pq$$
c)
$$9x^2 - 15x^2 =$$ $$-6x^2$$
d)
$$5cd - 13cd =$$ $$-8cd$$

Question 6

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, simplify the following:
a)$$-9x^2 - 6x^2 =$$
b)$$-8a^2 - 3a^2 =$$
c)$$-10m^3 - - 7m^3 =$$
d)$$- 14y^2 - - 11y^2 =$$

Answers

Show me your whiteboards.
a)
$$- 9x^2 - 6x^2 =$$ $$-15x^2$$
b)
$$-8a^2 - 3a^2 =$$ $$-8a^2$$
c)
$$-10m^3 - - 7m^3 =$$ $$-3m^3$$
d)
$$- 14y^2 - - 11y^2 =$$ $$-3y^2$$

Core Knowledge

Sometimes we need to collect the same like terms multiple times within one expression. Work through the expression systematically, collecting all terms of the same type.

Example

Simplify the following:
a) $$3x^2 + 2x^2 + 7x^2 =$$ $$12x^2$$
b) $$5ab - 2ab + 4ab =$$ $$7ab$$

Example

Simplify the following:
c) $$4y^2 + 6y^2 - 3y^2 =$$
d) $$8mn - 3mn + 5mn =$$

Question 7

On your whiteboards, simplify the following:
a)$$6a^2 + 3a^2 + 5a^2 =$$
b)$$9pq - 4pq + 7pq =$$
c)$$8x^2 + 2x^2 - 5x^2 =$$
d)$$11cd - 6cd + 3cd =$$

Answers

Show me your whiteboards.
a)
$$6a^2 + 3a^2 + 5a^2 =$$ $$14a^2$$
b)
$$9pq - 4pq + 7pq =$$ $$12pq$$
c)
$$8x^2 + 2x^2 - 5x^2 =$$ $$5x^2$$
d)
$$11cd - 6cd + 3cd =$$ $$8cd$$

Question 8

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, simplify the following:
a)$$5x^2 + x^2 - 2x^2 =$$
b)$$7a^2 - 3a^2 + a^2 =$$
c)$$9m^3 + 2m^3 - 4m^3 =$$
d)$$6y^2 - y^2 + 3y^2 =$$

Answers

Show me your whiteboards.
a)
$$5x^2 + x^2 - 2x^2 =$$ $$4x^2$$
b)
$$7a^2 - 3a^2 + a^2 =$$ $$5a^2$$
c)
$$9m^3 + 2m^3 - 4m^3 =$$ $$7m^3$$
d)
$$6y^2 - y^2 + 3y^2 =$$ $$8y^2$$

Core Knowledge

In longer expressions with multiple different terms, we can sometimes collect like terms and simplify some parts. Look for terms that share the same variable parts.

Example

Can the following be simplified? Answer yes or no.
a) $$3a + 2b + 4c + 2d =$$ $$\text{No}$$
b) $$3a + 2b + 4c + 4a =$$ $$\text{Yes}$$

Example

Can the following be simplified? Answer yes or no.
c) $$3a + 2a + 4b + 3b =$$
d) $$3a + 4a + 2a + 4a =$$

Question 9

On your whiteboards, can the following be simplified? Answer yes or no.
a)$$5x + 3y + 2z + 4w =$$
b)$$6a^2 + 3b^2 + 2a^2 + 5c^2 =$$
c)$$4p + 7q + 3p + 2q =$$
d)$$8m + 4n + 3r + 5s =$$

Answers

Show me your whiteboards.
a)
$$5x + 3y + 2z + 4w =$$ $$\text{No}$$
b)
$$6a^2 + 3b^2 + 2a^2 + 5c^2 =$$ $$\text{Yes}$$
c)
$$4p + 7q + 3p + 2q =$$ $$\text{Yes}$$
d)
$$8m + 4n + 3r + 5s =$$ $$\text{No}$$

Question 10

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, can the following be simplified? Answer yes or no.
a)$$5a + 3a - 2b + 4b =$$
b)$$6x^2 - 2x^2 + 3y^2 - y^2 =$$
c)$$4m - 3m + 2n - n =$$
d)$$7p^2 + 2q^2 - 3p^2 + 4q^2 =$$

Answers

Show me your whiteboards.
a)
$$5a + 3a - 2b + 4b =$$ $$\text{Yes}$$
b)
$$6x^2 - 2x^2 + 3y^2 - y^2 =$$ $$\text{Yes}$$
c)
$$4m - 3m + 2n - n =$$ $$\text{Yes}$$
d)
$$7p^2 + 2q^2 - 3p^2 + 4q^2 =$$ $$\text{Yes}$$

Core Knowledge

When like terms are grouped together in an expression, collect each group separately. The expression may contain multiple different types of terms.

Example

Simplify the following:
a) $$4a + 3a + 2b + 4b =$$ $$7a + 6b$$
b) $$5x^2 + 2x^2 + 3y^2 + 6y^2 =$$ $$7x^2 + 9y^2$$

Example

Simplify the following:
c) $$6p + 2p + 5q + 3q =$$
d) $$8m^2 + 3m^2 + 4n^2 + 7n^2 =$$

Question 11

On your whiteboards, simplify the following:
a)$$7x + 4x + 3y + 5y =$$
b)$$9a^2 + 5a^2 + 6b^2 + 2b^2 =$$
c)$$8c + 6c + 4d + 7d =$$
d)$$10p^2 + 3p^2 + 5q^2 + 8q^2 =$$

Answers

Show me your whiteboards.
a)
$$7x + 4x + 3y + 5y =$$ $$11x + 8y$$
b)
$$9a^2 + 5a^2 + 6b^2 + 2b^2 =$$ $$14a^2 + 8b^2$$
c)
$$8c + 6c + 4d + 7d =$$ $$14c + 11d$$
d)
$$10p^2 + 3p^2 + 5q^2 + 8q^2 =$$ $$13p^2 + 13q^2$$

Question 12

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, simplify the following:
a)$$5a + 2a - 3b + 4b =$$
b)$$8x^2 - 3x^2 + 6y^2 - 2y^2 =$$
c)$$7m + m - 2n + 5n =$$
d)$$9p^3 - 4p^3 + 3q^3 - q^3 =$$

Answers

Show me your whiteboards.
a)
$$5a + 2a - 3b + 4b =$$ $$7a + b$$
b)
$$8x^2 - 3x^2 + 6y^2 - 2y^2 =$$ $$5x^2 + 4y^2$$
c)
$$7m + m - 2n + 5n =$$ $$8m + 3n$$
d)
$$9p^3 - 4p^3 + 3q^3 - q^3 =$$ $$5p^3 + 2q^3$$

Core Knowledge

Like terms don't always appear next to each other. Look through the entire expression to find and collect all like terms, even when they're separated by other terms.

Example

Simplify the following:
a) $$3a^2 + 4b + 6a^2 + 2b =$$ $$9a^2 + 6b$$
b) $$5x + 7y + 2x + 3y =$$ $$7x + 10y$$

Example

Simplify the following:
c) $$8p^2 + 3q + 4p^2 + 5q =$$
d) $$6m + 9n + 5m + 2n =$$

Question 13

On your whiteboards, simplify the following:
a)$$7a^2 + 5b + 3a^2 + 4b =$$
b)$$9x + 6y + 4x + 2y =$$
c)$$8c^2 + 3d + 6c^2 + 7d =$$
d)$$10p + 5q + 7p + 3q =$$

Answers

Show me your whiteboards.
a)
$$7a^2 + 5b + 3a^2 + 4b =$$ $$10a^2 + 9b$$
b)
$$9x + 6y + 4x + 2y =$$ $$13x + 8y$$
c)
$$8c^2 + 3d + 6c^2 + 7d =$$ $$14c^2 + 10d$$
d)
$$10p + 5q + 7p + 3q =$$ $$17p + 8q$$

Question 14

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, simplify the following:
a)$$6x^2 + 7 + 2 + 3x^2 =$$
b)$$5a + 9 + 4 + 7a =$$
c)$$8m^2 + 3 + 6m^2 + 5 + 2m^2 =$$
d)$$4y + 12 + 7y + 8 + 3y =$$

Answers

Show me your whiteboards.
a)
$$6x^2 + 7 + 2 + 3x^2 =$$ $$9x^2 + 9$$
b)
$$5a + 9 + 4 + 7a =$$ $$12a + 13$$
c)
$$8m^2 + 3 + 6m^2 + 5 + 2m^2 =$$ $$16m^2 + 8$$
d)
$$4y + 12 + 7y + 8 + 3y =$$ $$14y + 20$$

Core Knowledge

When collecting like terms, the result can be a negative coefficient if we're subtracting a larger coefficient from a smaller one. For example, $3x - 5x = -2x$.

Example

Simplify the following:
a) $$6x^2 - 9x^2 =$$ $$-3x^2$$
b) $$4ab - 7ab =$$ $$-3ab$$

Example

Simplify the following:
c) $$5y^2 - 8y^2 =$$
d) $$3mn - 11mn =$$

Question 15

On your whiteboards, simplify the following:
a)$$7a^2 - 10a^2 =$$
b)$$4pq - 9pq =$$
c)$$8x^2 - 12x^2 =$$
d)$$5cd - 13cd =$$

Answers

Show me your whiteboards.
a)
$$7a^2 - 10a^2 =$$ $$-3a^2$$
b)
$$4pq - 9pq =$$ $$-5pq$$
c)
$$8x^2 - 12x^2 =$$ $$-4x^2$$
d)
$$5cd - 13cd =$$ $$-8cd$$

Question 16

You haven't seen questions exactly like this before, but using what you know, on your whiteboards, simplify the following:
a)$$6x^2 - 2a - 3x^2 - 12a =$$
b)$$5m + 7n - 9m - 3n =$$
c)$$8p^2 - 4q^2 - 11p^2 + 2q^2 =$$
d)$$4c - 9d - 7c + 5d =$$

Answers

Show me your whiteboards.
a)
$$6x^2 - 2a - 3x^2 - 12a =$$ $$3x^2 - 14a$$
b)
$$5m + 7n - 9m - 3n =$$ $$-4m + 4n$$
c)
$$8p^2 - 4q^2 - 11p^2 + 2q^2 =$$ $$-3p^2 - 2q^2$$
d)
$$4c - 9d - 7c + 5d =$$ $$-3c - 4d$$

📝 Core Knowledge Review - Write in your books:

Like terms: Terms are like terms when they have exactly the same variable parts. Only like terms can be collected together.
Collecting like terms: Add or subtract the coefficients and keep the variable part unchanged. Example: $3x^2 + 2x^2 = 5x^2$.
Negative results: When subtracting, the result can be negative. Example: $4a^2 - 10a^2 = -6a^2$.
Multiple families: Collect each family of like terms separately, even when they're mixed. Example: $5x + 3y + 2x + 4y = 7x + 7y$.

Independent Apply Task

Complete all questions on the worksheet showing all working out.
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