Writing and Simplifying Algebraic Expressions

Writing Phrases as an Algebraic Expression 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. 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 (x 2 )

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 x Eight more 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.

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: + 3x 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 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.

Combining Like Terms What is a term? –A term can be any combination of a number (coefficient), variable(s), and exponents. Examples: 2, 3x, 4x 2, 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 7x + 3x They are like terms (both have an x variable) so we simply add the coefficients together giving us 10x 10y 2 + 2y 2 Again, they are like terms (y 2 ) because the variables are the same. So we simply add the coefficients together giving us 12y 2

List the like terms in each set: Set 1 5x7y76y5x4123y Set 2 4xy9x4x 2 y4y613yx5yx 2 17x Set 3 9y 2 z4yz8zy 2 8zy9z2yz 5yx 2 5x

List the like terms in each set: Set 1 5x7y76y5x4123y Answers: 5x and 5x; 7y, 6y, and 3y; 7, 4, and 12 Set 2 4xy9x4x 2 y4y613yx5yx 2 17x Answers: 4xy and 13yx; 9x and 17x; 4x 2 y and 5yx 2 ; 4y; 6 Set 3 9y 2 z4yz8zy 2 8zy9z2yz 5yx 2 5x Answers: 9y 2 z and 8zy 2 ; 4yz, 8zy, and 2yz; 9z; 5yx 2 ; 5x

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 1.11b – 9a – 6b 2.7x + 5y – 4x – 4y 3.4a + 7b + 3 – 2a + 3b – a a m 2 – 3m + 6m 2 6.5p 2 + 2p p 2 + 5p – 6 7.Subtract 12a 3 from 15a 3 8.Subtract 8ab from the sum of 7ab and 5ab 9.17r 3 s 2 -8r 3 s 2 10.Subtract 4x 2 y from the sum of 6x 2 y and 12x 2 y Do the work and then check your answers on the next slide.

Answers to Adding and Subtracting Like Terms 1.5b – 9a 2.3x + y 3.2a + 10b a m 2 – 3m 6.9p 2 + 7p a 3 8.4ab 9.9r 3 s x 2 y