Unit 5 sec 3.1 simplifying terms and simplifying single term

Unit 5 sec 3.1 simplifying terms and simplifying single term

17 December 2015

00:01

Sometimes the terms in an expression need to be simplified, to make the expression easier to work with, and to make it easy to recognise any right terms.

  Term consists of numbers and letters are multiplied together, then it should be written with a coefficient 1^st, followed by the letters. It is often useful to write the letters in alphabetical order. For example, 3B²DA as 3AB²D. This can help you to identify right terms in a complicated expression.

Term includes a letter multiplied by itself, then index notation should be used. For example,

P × P should be simplified to P²

And

P × P × P should be simplified to P³

Example 6 simplifying terms

write the following terms in the shortest forms.

(A)       3 × c × g ×4 ×b

(B)      B × a × 5 × b × b

Solution

(A)       3 × c × g ×4 ×b = 12bcg

(B)      B × a × 5 × b × b = 5ab³

When you simplify a term you should normally use index notation only for letters, not for numbers. For example

3 × 3 × a should be simplified to 9a, not 3²a.

Example 7 multiplying powers

trying to the following term in his shortest form:

2AB × 3AB.

Solution

2AB × 3AB = 2 × 3 ×a 5+4b1+7 = 6a9b8

With multiplying or dividing:

2 signs the same give a plus sign

2 different signs and minus sign.

Example 8 simplifying terms involving minus signs

write the following terms in the shortest forms

a)  4q × (-2p)

b)  -B³ × (-5B)

c)   -A × (-B) × (-A)

Solution

a)  a positive times in negative games and negative            4q × (-2p) = 4q × 2p = -8pq

b)  a negative times negative gives a positive                  -B³ × (-5B) = + b³ × 5b = +5b4

c)  the 1^st negative times the 2^nd negative gives a positive, then positive times the 3^rd negative gives a negative

-A × (-B) × (-A) = -a × b × a = -a²b

Strategy to simplify a term

1)  finding the overall sign and write it at front.

2)  Simplify the rest of the coefficient and write it next.

3)  Write the letters in alphabetical order (usually), using index notation as appropriate.

Expressions can contain terms of the form

+ (-something) or – (-something).

These should be simplified by using the following facts.

v Adding the negative of something is the same as subtracting the something.

v Subtracting the negative of something is the same as adding the something.