Is there more factoring to come?

  • MHB
  • Thread starter mathdad
  • Start date
  • Tags
    Grouping
In summary, the expression a^2t^2 + b^2t^2 - cb^2 - ca^2 can be factored by grouping into (t^2 - c)(a^2 + b^2).
  • #1
mathdad
1,283
1
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 48.

Factor the expression by grouping.

a^2t^2 + b^2t^2 - cb^2 - ca^2

Group A = a^2t^2 + b^2t^2

Group A = t^2(a^2 + b^2)

Group B = -cb^2 - ca^2

Group B = -c(b^2 + a^2)

Group B = -c(a^2 + b^2)

Group A - Group B

t^2(a^2 + b^2) - c(a^2 + b^2)

(t^2 - c)(a^2 + b^2)

Correct?
 
Mathematics news on Phys.org
  • #2
RTCNTC said:
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 48.

Factor the expression by grouping.

a^2t^2 + b^2t^2 - cb^2 - ca^2

Group A = a^2t^2 + b^2t^2

Group A = t^2(a^2 + b^2)

Group B = -cb^2 - ca^2

Group B = -c(b^2 + a^2)

Group B = -c(a^2 + b^2)

Group A - Group B

t^2(a^2 + b^2) - c(a^2 + b^2)

(t^2 - c)(a^2 + b^2)

Correct?

yes
 
  • #3
More factoring coming in the next few days.
 

1. What is factor by grouping?

Factor by grouping is a method used in algebra to factor polynomials with four or more terms. It involves grouping terms together and factoring out the common factor.

2. When do you use factor by grouping?

Factor by grouping is used when a polynomial has four or more terms and can be grouped into pairs with a common factor. It is an alternative method to factoring using the GCF (greatest common factor).

3. How do you factor by grouping?

To factor by grouping, first group the terms in pairs, then factor out the common factor from each pair. Finally, factor out the common factor from the remaining terms, and combine the factors to find the final answer.

4. What are the benefits of using factor by grouping?

Factor by grouping is useful when a polynomial has four or more terms and can be grouped into pairs. It can also help simplify complex polynomials and make them easier to solve.

5. Are there any limitations to factor by grouping?

Factor by grouping can only be used when a polynomial has four or more terms and can be grouped into pairs. It is not applicable to all types of polynomials and may not always result in a simplified form.

Similar threads

MHB Yes, your factorization is correct.
    • General Math
Replies
4
Views
1K
A Explicit example of two complex numbers for double cover U(1) of SO(2) for a specified angle
    • General Math
Replies
2
Views
406
MHB Is it necessary to expand the quantity before factoring the expression?
    • General Math
Replies
6
Views
1K
MHB -c5.LCM and Prime Factorization of A,B,C
    • General Math
Replies
3
Views
557
MHB How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?
    • General Math
Replies
2
Views
989
MHB How do you factor a cubic function?
    • General Math
Replies
2
Views
1K
I Understanding Lorentz Groups and some key subgroups
    • General Math
Replies
3
Views
1K
MHB How do I factor this expression: 3(x + 5)^3 + 2(x + 5)^2?
    • General Math
Replies
3
Views
1K
B Looking for context for a textbook quote
    • General Math
Replies
9
Views
1K
MHB Is 27 - (a - b)^3 a Difference of Cubes in Precalculus?
    • General Math
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top