Week 5: Distributing, like terms, exponents, and roots
Field Book
17 to 20
Due
Test 3 due
Method
Paper first, every step
Expressions get shorter this week: distribute, then gather the terms that match. Exponents give repeated multiplication a shorthand, and roots run the squaring machine backward.
What you have to be able to do
Distribute and then collect like terms
Evaluate powers
Give the square root of a perfect square
The procedures
Collecting like terms
Like terms share the exact same letter part.
Add or subtract their coefficients; the letter part does not change.
Unlike terms just stand next to each other, joined by their signs.
Exponents
The base is the number being repeated; the exponent counts the repeats.
52 means 5 × 5, not 5 × 2.
An exponent touches only what it is written on, unless a grouping says otherwise.
Square roots
The square root of a number is what multiplies by itself to give it.
Know the perfect squares to at least 144 on sight.
Rooting undoes squaring, the way subtraction undoes addition.
Worked
WORKED
Simplify 3(2x + 5) − 4x. Distribute: 6x + 15 − 4x. Collect the x terms: 6x − 4x is 2x. ANSWER: 2x + 15
WORKED
Evaluate 52 − the square root of 81. 52 is 25. The square root of 81 is 9. ANSWER: 16
Terms
Term
Meaning
coefficient
the number multiplying a variable
like terms
terms sharing the same letter part
exponent
the raised number counting repeated multiplication
base
the number an exponent repeats
square root
the number that multiplies by itself to give another
Check yourself
1. Simplify: 7x + 2 − 3x
2. Evaluate 33
3. Give the square root of 64
reveal answers
4x + 2 · 27 · 8
This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.
-- THE UNKNOWN -- week 5, distributing, like terms, exponents, and rootsalgebra 1 · oda