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mathematics UK Year 9 Mathematics (KS3)

Solved problems for the chapter:

Factorising simple algebraic expressions

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Integers for KS3

open

1. Presenting integers on a number line

2. Arithmetic operations of integers

2.1. Subtraction of Integers

2.2. Properties of arithmetic operations

2.2.1. Existence of an identity element

2.2.2. The sum of any integer and its additive inverse

2.2.3. The negation of an additive inverse is its positive value

2.2.4. The additive inverse of a sum

2.2.5. Identity element for multiplication

2.2.6. Multiplication by (-1)

2.2.7. Multiplication by 0

2.2.8. The product of positive and negative integers

2.2.9. The product of a negative and a positive integer

3. Removing brackets

4. Order of integers

4.1. Greater than " > "

4.2. Less than " < "

4.3. Equals to " = "

4.4. Less than or equal to "

4.5. Greater than or equal to " >= "

4.5.1. Properties of "Less than"

4.5.2. Properties of "less than or equal to"

4.5.3. Properties of "greater than or equal to"

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Multiples and expressions for KS4

open

1. Monomials, binomials and multinomials

2. Breaking down numbers

2.1. Breaking down numbers into prime factors

3. Calculating expressions

3.1. The square of the sum of two terms

3.2. The square of the difference of two terms

3.3. The cube of a binomial

3.4. The difference of squares

3.5. The difference of cubes

3.6. The sum of cubes

3.7. Difference of n-th power

3.8. Vieta's formula

4. Exposing common factors

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Natural numbers for KS4

open

1. Representation of natural numbers on a number line

1.1. Calculation operations of natural numbers

1.1.1. Addition of natural numbers

1.1.2. Multiplication of natural numbers

1.2. Properties of arithmetic operations

1.2.1. Commutative property

1.2.2. Associative law or factor aggregation law

1.2.3. Distribution law

1.2.4. Existence of a neutral multiplier element

2. Prime numbers and compound numbers

2.1. Product of prime factors

2.2. Factorizing the common factor

↓ Show theory [3] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:factorising_simple_algebraic_expressions/5244/

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorize:

Factorise:

Factorise:

Factorise:

Factorise:

Factorise:

Factorise:

Factorize:

Rewrite using the common factor:

Rewrite using the common factor:

Express using the common factor:

Express using the common factor:

Express using the common factor:

Express using the common factor:

Factorize using the highest common factor:

Factorize: