Is there more factoring to come?

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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
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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?
 
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  • #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.
 

FAQ: Is there more factoring to come?

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.

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).

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.

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.

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.

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