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This pdf includes the following topics:-

Expanding brackets

FOIL

Distributive Law

Distributive properties

Examples

Expanding brackets

FOIL

Distributive Law

Distributive properties

Examples

1.
Student

Learning Expanding Brackets

Centre

Expanding brackets

Expanding is to remove brackets from an algebraic expression.

FOIL is called the Distributive Law: (a+b)(c+d) = ac+ad+bc+bd

FOIL

Expand

For example :

factoring 2y + 6

2 𝑦𝑦 + 3 2𝑦𝑦 + 6 both 2y and 6 have a common factor of 2

2y is 2 × y

6 is 2 × 3

So you can factor the whole expression into: 2y+6 = 2(y+3)

Factor

Find the product (m – 1)(-4m – 4)

To simplify the product of two binomials, use the distributive property.

Use the FOIL method. Find the products of the First, Outside, Inside, and Last terms, and then add them.

Use the distributive property to simplify (m – 1)(-4m – 4). You can use the FOIL method:

Multiply the first terms of (m – 1)(-4m – 4): (m)(-4m) = -4m2

Multiply the outside terms of (m – 1)(-4m – 4): (m)(-4) = -4m

Multiply the inside terms of (m – 1)(-4m – 4): (-1)(-4m) = 4m

Multiply the last terms of (m – 1)(-4m – 4) : (-1)(-4) = 4

Finally, add these results and simplify.

-4m2 + -4m + 4m + 4

-4m2 + 4

Expanding Brackets 5/2013 @ SLC 1 of 2

Learning Expanding Brackets

Centre

Expanding brackets

Expanding is to remove brackets from an algebraic expression.

FOIL is called the Distributive Law: (a+b)(c+d) = ac+ad+bc+bd

FOIL

Expand

For example :

factoring 2y + 6

2 𝑦𝑦 + 3 2𝑦𝑦 + 6 both 2y and 6 have a common factor of 2

2y is 2 × y

6 is 2 × 3

So you can factor the whole expression into: 2y+6 = 2(y+3)

Factor

Find the product (m – 1)(-4m – 4)

To simplify the product of two binomials, use the distributive property.

Use the FOIL method. Find the products of the First, Outside, Inside, and Last terms, and then add them.

Use the distributive property to simplify (m – 1)(-4m – 4). You can use the FOIL method:

Multiply the first terms of (m – 1)(-4m – 4): (m)(-4m) = -4m2

Multiply the outside terms of (m – 1)(-4m – 4): (m)(-4) = -4m

Multiply the inside terms of (m – 1)(-4m – 4): (-1)(-4m) = 4m

Multiply the last terms of (m – 1)(-4m – 4) : (-1)(-4) = 4

Finally, add these results and simplify.

-4m2 + -4m + 4m + 4

-4m2 + 4

Expanding Brackets 5/2013 @ SLC 1 of 2

2.
DISTRIBUTIVE PROPERTIES

The Distributive Properties rules tell us that if you have a term being multiplied by two or more terms being

either added or subtracted within brackets (parenthesis), the term outside the brackets must be multiplied by

EVERY term within the brackets.

STUDENT LEARNING CENTRE

REGISTRY BUILDING ANNEXE

TEL: 61-8-8201 2518

E-MAIL: [email protected]

INTERNET: http://www.flinders.edu.au/SLC

POSTAL: PO BOX 2100, ADELAIDE, SA 5001

Expanding Brackets 5/2013 @ SLC 2 of 2

The Distributive Properties rules tell us that if you have a term being multiplied by two or more terms being

either added or subtracted within brackets (parenthesis), the term outside the brackets must be multiplied by

EVERY term within the brackets.

STUDENT LEARNING CENTRE

REGISTRY BUILDING ANNEXE

TEL: 61-8-8201 2518

E-MAIL: [email protected]

INTERNET: http://www.flinders.edu.au/SLC

POSTAL: PO BOX 2100, ADELAIDE, SA 5001

Expanding Brackets 5/2013 @ SLC 2 of 2