Unit 5 sec 3.2 simplifying two or more terms

Unit 5 sec 3.2 simplifying two or more terms

20 December 2015

22:41

To simplify an expression with 2 or more terms, you need to simplify each turn individually, in the way that you have seen. Before you can do that you need to identify which bits of the expression belonging to which term.

Each term after the 1^st starts with a plus or - that is not inside brackets.

Example 9 identifying terms

Mark the terms in the following expressions

a)  -2a - (5a²) + (-4a)

b)  2x × 4xy – 2y × (-5x)

Solution

a)  Begin by marking the start of the 1^st term                 -2a - (5a²) + (-4a)

extended the line under the 1^st term until you reach a plus or minus sign that is not inside brackets. That is the start of the next term

-2a - (5a²) + (-4a)

extend the line under the 2^nd term until you reach a plus or - that is not inside brackets. That is the start of the next term

-2a - (5a²) + (-4a)

extend the line under the 3^rd time until you reach a plus or minus sign that is not inside brackets. This time you do not reach 1 you just reach the end of the expression. So this expression has 3 terms

-2a - (5a²) + (-4a).

b)  Mark the start of the 1^st term

2x × 4xy – 2y × (-5x)

when you reach a plus or - that is not inside brackets that the start of the next term

2x × 4xy – 2y × (-5x)

you do not to reach another plus or - that is not inside brackets, so this expression has to terms.

2x × 4xy – 2y × (-5x).

Strategy to simplify an expression with more than one term

1)  identify the term. Each term after the 1^st starts with a plus or - that is not inside brackets.

2)  Simplify each term, using this strategy on page 22. Include this sign (plus or minus) at the start of each term.

3)  Any like terms.

Example 10 simplifying expressions with more than one term.

Simplify the following expressions.

(A)       -2a - (-5a²) + (-4a)

(B)      2x × 4xy – 2y × (-5x)

Solution

(A)       1^st, identify the terms . Then simplify each term individually. Finally, collect like terms

-2a - (-5a²) + (-4a) = -2a + 5a² - 4a = 5a² - 6a

this could also be written as -6a + 5a²

(B)      identifying the terms, then simplify each term individually. Finally, check for like terms  - there are non here

-2x × 4xy – 2y × (-5x) = 8x²y + 10y