Algebra 1: Chapter 1, Lesson 5, page 24.
Distributive Property of Mutiplication over Addition
The distributive property of mulitplication over addition is written as `a(b+c)=ab+ac`. For example:
`3(x+2)=3x+6`
The opposite of distribution is factoring where we go backward. For example:
`3x+3y=3(x+y)`
In an expression like `6s+6t+6w`, the `6s`, `6t` and `6w` are called terms. Like terms are terms with like variables THAT HAVE THE SAME EXPONENT!
You can collect like terms, for example:
`6y^2+2y^2` is the same as `8y^2`
and `4x^3+5x^3` is the same as `9x^3`
Try these 2 links from purplemath.com, this one for distribution and this one for factoring.
Two of tonight’s homework problems solved by MrE are here! Just click it!!
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Algebra 1a: Chapter 1, Lesson 3, page 15.
Exponential Notation
A product in which the factors are the same is called a power. We can write `2⋅2⋅2⋅2` as `2^4`. The number 4 is called the exponent and the 2 is called the base. The exponent tells how many times the base is used as a factor. When an expression is written with exponents, we say the expression is written using exponential notation.
Remember, anything to the zero power is = 1, `z^0=1` or `4^0=1` as well. Anything raised to the 1 power is just the number, `y^1=y` and `101^1=101`.
Don’t forget PEMDAS too with the exponents being the second operation to be performed.
I like to use a site called purplemath.com. They have some great explanations about our lessons. See these explanations on exponents too!
Two of tonight’s homework problems solved by MrE are here! Just click it!!