Unit #1

Expressions

Definition

Algebraic ExpressionAn algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply, and divide). 

Here are some algebraic expressions: 

a + 1

a - b

3x

x - a / b

In the above expression the "/" means divide. The "3x" means multiply the variable x by 3.

Many English phrases translate directly into algebraic expressions, as shown in the following (where x stands for "a number"):

English expression: A number plus eight Equivalent Algebraic expression: x + 8English expression: Four less than a numberEquivalent Algebraic expression: x – 4 English expression: half of a numberEquivalent Algebraic expression: x / 2

If you set an algebraic expression equal to something, with an equal sign, you now have an equation, like:

X - 4 = 10

NOTE:

Simplify the following:

1. -9n -n -3m

2. 3ab -2ac +4ab

3. 2a -4b +3ab -5a +2b

TRY THESE

1. Remember, there is technically a coefficient of 1 before the – n.

-9n – 1n – 3m

Answer: -10n – 3m

2. Rewrite with like terms together

3ab - 2ac + 4ab3ab + 4ab – 2ac

Answer: 7ab – 2ac

3. Rewrite with like terms together

2a -4b +3ab -5a +2b2a - 5a + 3ab -4b + 2b

Answer: -3a + 3ab - 2b

Class work:4. 8x -9y -3xy - 2y -x +4xy

5. 2r -3s -t +3t +3s

6. 4(2p -1) - (p+5)

7. 6(p +3q) - (7 +4q)

8. 2(xy -1) + 3(x-2y) -4xy

9. 4rs -2s -3(rs +1) -2s

10. 8y -2z -(y-z)+3yz

Answers:

4)7x -11y + xy

5)2r + 2t

6)7p – 9

7)6p +14q -7

8)-2xy +3x -6y – 2

9)rs – 4s – 3

10)7y – z + 3yz

Algebraic expressionsReal challenges in science or in business occur in ordinary language.  To solve such challenges, we typically have to translate them into algebraic language.Challenge 9.   Write an algebraic expression that will symbolize each of the following.a)   Six times a certain number..b)  Six more than a certain number.  c)  Six less than a certain number.  d)  Six minus a certain number.  e)  A number repeated as a factor three times.  f)  A number repeated as a term three times.  g)   The sum of three consecutive whole numbers. The idea, for example, of  6 + 7 + 8.  [Hint:  Let x be the first number.] h)  Eight less than twice a certain number.  i)  One more than three times a certain number.

Algebraic expressionsReal challenges in science or in business occur in ordinary language.  To solve such challenges, we typically have to translate them into algebraic language.Challenge 9.   Write an algebraic expression that will symbolize each of the following.a)   Six times a certain number.   6n, or 6x, or 6m. Any letter will do.b)  Six more than a certain number.   x + 6c)  Six less than a certain number.   x − 6d)  Six minus a certain number.   6 − xe)  A number repeated as a factor three times.   x· x· x = x3

f)  A number repeated as a term three times.   x + x + x = 3xg)   The sum of three consecutive whole numbers. The idea, for example, of  6 + 7 + 8.  [Hint:  Let x be the first number.]    x + (x + 1) + (x + 2)h)  Eight less than twice a certain number.   2x − 8i)  One more than three times a certain number.   3x+1 

Factoring Expressions game

https://www.mangahigh.com/en-us/math_games/algebra/factoring/factor_using_a_common_term