factoring variable equations
- Thread starter artluvr77
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mmm4444bot
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First, some comments about terminology.
These are not equations. Equations always contain an equals sign.
These are expressions (in general) and polynomials (in particular).
We cannot factor all of these expressions because some of them are not factorable.
Do you understand the concepts of "factor" and "product"?
Do you understand that factoring is the reverse of the Distributive Property? (Do you remember the Distributive Property?)
Are you familiar with the FOIL algorithm for multiplying two binomials? FOIL shows us how to apply the distributive property twice. If you don't first understand FOIL, then understanding how to factor these types of expressions is very difficult.
Are you familiar with any of the special factoring patterns (eg: difference of squares, sum of cubes, difference of cubes, squared binomial, et cetera)?
I would like to know more about what you already know, before I decide where to begin helping you further.
?
x^2 y + x y^2
Each of these terms contain at least one factor of x and one factor of y, so xy can be factored out.
In other words, this expression is the product of the factor xy and a binomial. (Think in terms of the Distributive Property.)
xy * ( ___ + ___ )
Fill in the two blanks, such that use of the Distributive Property brings you back to the given expression.
Please let us know what you already know.
These are not equations. Equations always contain an equals sign.
These are expressions (in general) and polynomials (in particular).
We cannot factor all of these expressions because some of them are not factorable.
Do you understand the concepts of "factor" and "product"?
Do you understand that factoring is the reverse of the Distributive Property? (Do you remember the Distributive Property?)
Are you familiar with the FOIL algorithm for multiplying two binomials? FOIL shows us how to apply the distributive property twice. If you don't first understand FOIL, then understanding how to factor these types of expressions is very difficult.
Are you familiar with any of the special factoring patterns (eg: difference of squares, sum of cubes, difference of cubes, squared binomial, et cetera)?
I would like to know more about what you already know, before I decide where to begin helping you further.
?
artluvr77 said:
x^2 y + x y^2
Each of these terms contain at least one factor of x and one factor of y, so xy can be factored out.
In other words, this expression is the product of the factor xy and a binomial. (Think in terms of the Distributive Property.)
xy * ( ___ + ___ )
Fill in the two blanks, such that use of the Distributive Property brings you back to the given expression.
Please let us know what you already know.
artluvr77 said:i need help factoring these equationsyou can pick a couple just so i get how to do them i forget)
a²+12a+3b
4a²+4a+1
121y²+22y+1
9a²+6a+2
6x²+18x+24
x³-27
x³y³+64
8x³-9y³
x³-y³
x²y+xy²
8x³-36x²y+54xy²-27y³
xy+x²y-6x³y
You've posted a wide variety of problems, covering MANY types of factoring.
We can't teach topics here. Please take these problems, one at a time, and show us what you've tried, so we can see where you need help.
mmm4444bot
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artluvr77 said:
x^2 y + x y^2 = xy * ( ___ + ___ )
If you understand the Distributive Property, and you just claimed that you do, then you know how to fill in the blanks above.
Show me what you get.
Here's help on another one.
x^3 - y^3
Look up "difference of cubes" in your textbook's index (or use Google). There's your answer.