Lesson 2: Multiplying terms (the basics)

Introduction

In this lesson, we are going to be multiplying terms together and writing the answer in its simplest form. The lesson is divided into two sections.

SECTION A

Follow these rules and you will be able to multiply simple terms.

1. Get rid of multiplication signs.

       \(a\times b\times c~=~abc\)

2. If there is a number, write this first.

       \(x\times 2~=~2x\)

3. If there is more than one number, multiply them together and write the answer first.

       \(3\times c\times 6~=~18c\)

4. If there is more than one letter, write them in alphabetical order.

       \(r\times p\times q~=~pqr\)

Practise to master

SECTION A

Simplify each of these using your knowledge of multiplying terms.

01)  \(5\times d\)

\(5d\)

02)  \(c\times 7\)

\(7c\)

03)  \(0\times t\)

\(0\)
Because anything multiplied by zero equals zero!

04)  \(y\times 1\)

\(y\)
Since \(y\) and 1\(y\) are equivalent, we don't write the 1.

05)  \(3\times 2\times n\)

\(6n\)

06)  \(5\times w\times 2\)

\(10w\)

07)  \(m\times 6\times 2\)

\(12m\)

08)  \(2\times g\times 3\times 4\)

\(24g\)

09)  \(y\times x\)

\(xy\)

10)  \(c\times a\)

\(ac\)

11)  \(p\times r\times q\)

\(pqr\)

12)  \(w\times u\times v\times y\)

\(uvwy\)

13)  \(b\times 5\times a\)

\(5ab\)

14)  \(2\times e\times 2\times d\)

\(4de\)

15)  \(4\times g\times a\times 3\)

\(12ag\)

16)  \(r\times 4\times p\times 5\times q\)

\(20pqr\)

SECTION B

Now let's learn how to multiply terms that aren't quite so simple.

5. If any terms are already a combination of a number and letter(s), unsimplify these first.

       \(2bc\times 3a~=~2\times b\times c\times 3\times a\)
       \(2bc\times 3a\)\(~=~2\times 3\times a\times b\times c\)
       \(2bc\times 3a\)\(~=~6abc\)

(If there is more than one of the same letter, we use indices to combine them - but that's what next lesson is about!)

Practise to master

SECTION B

Simplify each of these using your knowledge of multiplying terms.

01)  \(2\times 5a\)

\(10a\)

02)  \(3b\times 1\)

\(3b\)

03)  \(3c\times 5\)

\(15c\)

04)  \(3\times 2d\times 2\)

\(12d\)

05)  \(v\times uw\)

\(uvw\)

06)  \(st\times r\)

\(rst\)

07)  \(e\times d\times gh\)

\(degh\)

08)  \(be\times c\times ad\)

\(abcde\)

09)  \(3r\times pq\)

\(3pqr\)

10)  \(2x\times 4y\)

\(8xy\)

11)  \(7y\times 3ab\)

\(21aby\)

12)  \(6mp\times 3nq\)

\(18mnpq\)

13)  \(4r\times 2p\times 3q\)

\(24pqr\)

14)  \(c\times 4ab\times 5d\)

\(20abcd\)

15)  \(2xz\times 3y\times 3\)

\(18xyz\)

16)  \(2ab\times 4d\times ce\)

\(8abcde\)

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