39
Rule for removing brackets. The coefficient
Textbook, pp. 182–185
GoalKnow the rule for removing brackets; understand coefficients and combine like terms.
New words
removing brackets · qavslarni ochishcoefficient · koeffitsiyentlike terms · o‘xshash hadlarsimplifying · ixchamlash
Explanation
If there is a “+” sign in front of a bracket, removing it leaves the signs inside unchanged: a + (b − c) = a + b − c. If there is a “−” sign in front, every sign inside the bracket changes to its opposite: a − (b − c) = a − b + c. In a letter expression the numerical factor is the coefficient: in 5x it is 5, in −7y it is −7, in x it is 1 and in −x it is −1. Terms with the same letter part are like terms: 3x + 5x = 8x. We add the coefficients and keep the letter part.
Worked examples
15 − (7 − 4) = 15 − 7 + 4 = 12. Check: 7 − 4 = 3 and 15 − 3 = 12.
4x + 7 − (x − 2) = 4x + 7 − x + 2 = 3x + 9.
Class activity
“Sign trap”: cards show expressions with brackets. One pupil removes the brackets and another checks by substituting a value (for example x = 2) that both expressions give the same result.
Practice
1
Compute 15 − (7 − 4) by removing the brackets.
12
2
State the coefficient of the term −7y.
−7
3
Simplify 4x + 7 − (x − 2).
3x + 9
4
Why do the signs inside change when a bracket with a “−” in front is removed?
The minus means subtracting the whole bracket, and subtracting is adding the opposite, so every term changes sign.