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Scott
Scott, MIT Graduate
Category: Math Homework
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How do you factor the difference of two squares? How do

Customer Question

How do you factor the difference of two squares?

How do you factor the perfect square trinomial?

How do you factor the sum and difference of two cubes?

Which of these three makes the most sense to you?

Explain why.

Please use t
Submitted: 3 years ago.
Category: Math Homework
Expert:  Scott replied 3 years ago.

Hi there,


The very end seems cut off: "Please use t"

 

Thanks,

Scott

Customer: replied 3 years ago.

Please make sure to answer all components of each question. Please DO NOT attach any DQ responses. Respond within the forum.


How do you factor the difference of two squares?


How do you factor the perfect square trinomial?


How do you factor the sum and difference of two cubes?


Which of these three makes the most sense to you?


Explain why.


Please use the "Quote Original" feature when responding to ALL threads, as this will make it easier to follow the discussion. Also, please remember to answer all parts of this DQ to assure full credit for your Discussion Question response. A minimum of 150- to 300 word response is required.


 


Out of a basic algebra II class


 

Expert:  Scott replied 3 years ago.

Hi there,

 

How do you factor the difference of two squares?

A difference of squares is a two term expression. It is in the form a^2-b^2, where "a" and "b" can contain numbers, variables, etc. To factor it, you use the formula (a-b)(a+b).

 

How do you factor the perfect square trinomial?

A perfect square trinomial is in the form a^2 + 2ab + b^2. Again, a and b can contain numbers and variables. In this case, you factor it as (a+b)^2, which is a perfect square. That's the same thing as (a+b)(a+b).

 

How do you factor the sum and difference of two cubes?

A sum of cubes is in the form a^3 + b^3. You factor it using the formula (a+b)(a^2 - ab + b^2).

A difference of cubes is in the form a^3 - b^3. You factor it using the formula (a-b)(a^2 + ab + b^2).

To help remember these two, the (a_b) term uses the same sign as the original problem, and the (a^2 _ ab + b^2) term uses the opposite sign for the _ symbol.

 

Which of these three makes the most sense to you? Explain why.

I think the difference of squares make the most sense and is the easiest to remember and use. It's a simple formula with two terms on the left side and two binomial factors on the right side. The key way I remember it is that it's a difference of squares, and the two binomial factors have different signs.

 

Let me know if you have any questions on this, and thanks for choosing a high rating!

-Scott