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Writing and Simplifying Algebraic Expressions. Writing Phrases as an Algebraic Expression. Key Words Added to, sum, increased, more than – means to add two things together Difference, subtracted from, minus – means to subtract Multiply, product of – means to multiply

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writing phrases as an algebraic expression

Writing Phrases as an Algebraic Expression

  • Key Words
  • Added to, sum, increased, more than – means to add two things together
  • Difference, subtracted from, minus – means to subtract
  • Multiply, product of – means to multiply
  • Quotient of, divided by – means to divide
  • Twice a number – means to multiply by 2
  • A number squared – means a number multiplied by itself twice (x2)

An expression does not contain an equal sign and cannot be solved, but it can be simplified.

An equation does contain an equal sign and can be solved.

let s try some phrases

Let’s try some phrases…

The difference of a number and two, divided by five.

Let’s write our numbers and signs above the statement.

- x 2 / 5

The difference of a number and two, divided by five.

When turning this phrase into an algebraic expression, we have to ask ourselves “The difference of what?” It is the difference between the x and 2 so it is written as x – 2.

Algebraically the second form is the correct form.

next phrase

Eight more than triple a number.

Let’s look at this phrase a different way.

8+3x

Eightmore than triple a number

The algebraic phrase would be 3x + 8. It is okay to write the phrase as 8 + 3x but 3x + 8 would be the correct algebraic form because we list our answers in order starting with the variables followed by the constants.

Next phrase…

and another one

The sum of 3 times a number and 10, subtracted from 9 times a number.

Again, let’s write things out above the phrase:

+ 3•x 10 - 9

The sum of 3 times a number and 10, subtracted from 9

• x

times a number.

Again, ask yourself “The sum of what?” That is the sum of 3x + 10. The subtracted from is very important here. Since it is stated this way, we are subtracting the first part “from” the second part or

9x – (3x + 10).

Why did a put the 3x+10 in parentheses? Because the problem states to subtract the “sum” of 3 times a number and 10. The minus sign outside the parentheses will then be changed to addition and the sign of everything inside will be changed to its opposite.

And another one…

combining like terms
Combining Like Terms
  • What is a term?
    • A term can be any combination of a number (coefficient), variable(s), and exponents. Examples: 2, 3x, 4x2, or 5xy
  • What are like terms?
    • Like terms have the exact same variables and exponents. Example: 3x and 7x both have the same variable “x” so they are like terms.
simplifying algebraic expressions

Simplifying Algebraic Expressions

10y2 + 2y2

Again, they are like terms (y2) because the variables are the same. So we simply add the coefficients together giving us

12y2

7x + 3x

They are like terms (both have an x variable) so we simply add the coefficients together giving us

10x

list the like terms in each set
List the like terms in each set:

Set 1

5x 7y 7 6y 5x 4 12 3y

Set 2

4xy 9x 4x2y 4y 6 13yx 5yx2 17x

Set 3

9y2z 4yz 8zy2 8zy 9z 2yz 5yx2 5x

list the like terms in each set9
List the like terms in each set:

Set 1

5x7y76y5x4123y

Answers: 5x and 5x; 7y, 6y, and 3y; 7, 4, and 12

Set 2

4xy9x4x2y4y613yx5yx217x

Answers: 4xy and 13yx; 9x and 17x; 4x2y and 5yx2; 4y; 6

Set 3

9y2z4yz8zy28zy9z2yz5yx25x

Answers: 9y2z and 8zy2; 4yz, 8zy, and 2yz; 9z; 5yx2; 5x

combining like terms recap
Combining Like Terms - Recap
  • Like terms are a combination of coefficients, variables, and exponents.
  • The variables and exponents of each number must match each other but they can be in a different order.
  • Once like terms are identified, you can then proceed to add or subtract their coefficients.
adding and subtracting like terms

11b – 9a – 6b

7x + 5y – 4x – 4y

4a + 7b + 3 – 2a + 3b – 2

2.3a + 7 + 4.7a + 3

5m2 – 3m + 6m2

5p2 + 2p + 8 + 4p2 + 5p – 6

Subtract 12a3 from 15a3

Subtract 8ab from the sum of 7ab and 5ab

17r3s2-8r3s2

Subtract 4x2y from the sum of 6x2y and 12x2y

Adding and Subtracting Like Terms

Do the work and then check your answers on the next slide.

answers to adding and subtracting like terms

5b – 9a

3x + y

2a + 10b +1

7a + 10

11m2 – 3m

9p2 + 7p + 2

3a3

4ab

9r3s2

14x2y

Answers to Adding and Subtracting Like Terms