collecting like terms lesson 31. terms literal coefficients – are variables (letters) that...

Collecting Like Terms

Lesson 31

Terms

• Literal Coefficients – are variables (letters) that represent unknown numbers.

• Numerical coefficients – are numbers

• Terms – are made up of numerical and literal coefficients.

Like Terms

• Terms with identical literal coefficients are like terms.

• EXAMPLE:• y, 3y, -2y are like terms• x, -2g, 3k are not like terms

• Basically the variable has to be the same.

Like Terms

• Also the variable needs to be to the same power to be like terms.

• Example:• y2, -2y2, 45y2 are like terms• y, -20y2, 5y3 are not like terms

• The exponent has to be the same number.

Try These

• Which are like terms? Why?

• 5b, 3g, -2g, 2g2, 5g, ½g, -g

Solution:

• Which are like terms? Why?

• 5b, 3g, -2g, 2g2, 5g, ½g, -g

• Red – like terms. ( they all have the same variable to the same power)

• White – not like terms.


In algebra we often get very long expressions, which we need to makesimpler. Simpler expressions are easier to solve!

Combining Like Terms

• t + t + t+ t + t

• There are five variables which are like terms therefore we simply add them like we would if they were numbers.

• t + t + t+ t + t = 5t


In algebra we often get very long expressions, which we need to makesimpler. Simpler expressions are easier to solve!To simplify an expression we collect like terms.


In algebra we often get very long expressions, which we need to makesimpler. Simpler expressions are easier to solve!To simplify an expression we collect like terms. ‘Like terms’ include letters that are the same and numbers.



Have a look at the expression 4x + 5x -2 - 2x + 7




All the x terms can be collected together to give 7x.




All the x terms can be collected together to give 7x. All the numbers collected together give 5.




All the x terms can be collected together to give 7x. All the numbers collected together give 5.So 4x + 5x -2 - 2x + 7 simplified is 7x + 5.


Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x



Here's how to do it in easy steps:



Here's how to do it in easy steps:• Write down the expression.

x + 5 + 3x - 7 + 9x + 3 - 4x




x + 5 + 3x - 7 + 9x + 3 - 4x• Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it.

x + 3x + 9x - 4x + 5 - 7 + 3





x + 3x + 9x - 4x + 5 - 7 + 3• Simplify the x terms.

x + 3x + 9x - 4x = 9x






x + 3x + 9x - 4x = 9x• Simplify the numbers separately.

5 - 7 + 3 = 1






x + 3x + 9x - 4x = 9x• Simplify the numbers separately.

5 - 7 + 3 = 1• The simplified expression is: 9x + 1


Eg:- Simplify this expression: 5x + 3y - 6x + 4y + 3z



•Collect the like terms together - ie, re-order them5x - 6x + 3y + 4y + 3z




•Simplify your expression, x first5x - 6x = -x





•then simplify y3y + 4y = 7y






•then simplify z3z






•then simplify z3z

•The answer is: -x + 7y + 3z.


We can extend this idea to terms involving powers, but we must remember the following rule:

x is not the same as x2



Eg:- Simplify the following expression 3x + 5 + x2 - 2x + 2x2 - 1





Rearrange the expression so that like terms are next to each other:

x2 + 2x2 + 3x - 2x + 5 - 1





Rearrange the expression so that like terms are next to each other:

x2 + 2x2 + 3x - 2x + 5 - 1

And then simplify:

NB: Expressions of this type are usually written with the 'x2' term first,

then the 'x' term and finally the number term.


3x2 + x + 4


Try these questions in your classwork books now:

Simplify the following:1) 4y + x – 2y – x + 3x2) x + 2x + 3y + 4z - y3) -y + 3z – 2y + 44) x + y2 + 2y – 7 – 2x + y5) 3xy + x2 + y – 2yx

collecting like terms lesson 31. terms literal coefficients – are variables (letters) that...

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