Easy Algebra Step-by-Step

Algebraic Expressions 71

If an opposite (−) symbol immediately precedes parentheses that enclose an

algebraic expression, remove the parentheses and the opposite symbol and

rewrite the algebraic expression, but with all the signs changed.

Problem Simplify −−⎛ +−

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

8 5 ⎞⎞⎞⎞

2

xy^3227

x

.

Solution

Step 1. Remove the parentheses and the oppo-

site symbol and rewrite the expression,

but change all the signs.

−−⎛ +−

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

8 5 ⎞⎞⎞⎞=−+

2

27 8

5

2

xy^323227

x

xy

x

If a minus (−) symbol immediately precedes parentheses that enclose an

algebraic expression, mentally think of the minus symbol as “+−,” meaning

“add the opposite.” Then remove the parentheses and rewrite the algebraic

expression, but change all the signs.

Problem Simplify 10 −() 373 3277 ++ 22.

Solution

Step 1. Mentally think of the minus symbol as “+−.”

10 +−() 3 3277777 2 ++ 22

Do this mentally.

  

Step 2. Remove the parentheses and rewrite the algebraic expression, but

with all the signs changed.

10 −() 3373277 ++ 22 = 10 − 373 xx^3277 − 2 x

If a number immediately precedes parentheses that enclose an algebraic

expression, apply the distributive property to remove the parentheses.

P

P

P

−−⎛ +−

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

8 5 ≠+−

2

27 8 5

2

xy^323227

x

y

x

.

Change all the signs, not just the fi rst

one. This mistake is very common.