Collecting Like Terms Lesson 31 Terms Literal Coefficients

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

Like Terms • Terms with identical literal coefficients are like terms. • EXAMPLE: •

Like Terms • Also the variable needs to be to the same power to

Try These • Which are like terms? Why? • 5 b, 3 g, -2

Solution: • Which are like terms? Why? • 5 b, 3 g, -2 g,

Collecting Like Terms In algebra we often get very long expressions, which we need

Combining Like Terms • t + t+ t • There are five variables which

Collecting Like Terms Eg: - Simplify this expression: x + 5 + 3 x

Collecting Like Terms Eg: - Simplify this expression: 5 x + 3 y -

Collecting Like Terms We can extend this idea to terms involving powers, but we

Collecting Like Terms Try these questions in your classwork books now: Simplify the following:

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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, 3 y, -2 y are like terms • x, -2 g, 3 k 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: • y 2, -2 y 2, 45 y 2 are like terms • y, -20 y 2, 5 y 3 are not like terms • The exponent has to be the same number.

Try These • Which are like terms? Why? • 5 b, 3 g, -2 g, 2 g 2, 5 g, ½g, -g

Solution: • Which are like terms? Why? • 5 b, 3 g, -2 g, 2 g 2, 5 g, ½g, -g • Red – like terms. ( they all have the same variable to the same power) • White – not like terms.

Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve!

Combining Like Terms • 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 = 5 t

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

Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. 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 4 x + 5 x -2 - 2 x + 7 All the x terms can be collected together to give 7 x.

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

Collecting Like Terms Eg: - Simplify this expression: x + 5 + 3 x - 7 + 9 x + 3 - 4 x Here's how to do it in easy steps:

Collecting Like Terms Eg: - Simplify this expression: x + 5 + 3 x - 7 + 9 x + 3 - 4 x Here's how to do it in easy steps: • Write down the expression. x + 5 + 3 x - 7 + 9 x + 3 - 4 x

Collecting Like Terms Eg: - Simplify this expression: x + 5 + 3 x - 7 + 9 x + 3 - 4 x Here's how to do it in easy steps: • Write down the expression. x + 5 + 3 x - 7 + 9 x + 3 - 4 x • Collect all the terms together which are alike. Remember that each term comes with an operation (+, -) which goes before it. x + 3 x + 9 x - 4 x + 5 - 7 + 3

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

Collecting Like Terms Eg: - Simplify this expression: 5 x + 3 y - 6 x + 4 y + 3 z • Collect the like terms together - ie, re-order them 5 x - 6 x + 3 y + 4 y + 3 z

Collecting Like Terms Eg: - Simplify this expression: 5 x + 3 y - 6 x + 4 y + 3 z • Collect the like terms together - ie, re-order them 5 x - 6 x + 3 y + 4 y + 3 z • Simplify your expression, x first 5 x - 6 x = -x • then simplify y 3 y + 4 y = 7 y

Collecting Like Terms We can extend this idea to terms involving powers, but we must remember the following rule: x is not the same as x 2

Collecting Like Terms We can extend this idea to terms involving powers, but we must remember the following rule: x is not the same as x 2 Eg: - Simplify the following expression 3 x + 5 + x 2 - 2 x + 2 x 2 - 1 Rearrange the expression so that like terms are next to each other: x 2 + 2 x 2 + 3 x - 2 x + 5 - 1 And then simplify: 3 x 2 + x + 4 NB: Expressions of this type are usually written with the 'x 2' term first, then the 'x' term and finally the number term.

Collecting Like Terms Try these questions in your classwork books now: Simplify the following: 1) 4 y + x – 2 y – x + 3 x 2) x + 2 x + 3 y + 4 z - y 3) -y + 3 z – 2 y + 4 4) x + y 2 + 2 y – 7 – 2 x + y 5) 3 xy + x 2 + y – 2 yx