MHB Is there more factoring to come?

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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). The first group, t^2(a^2 + b^2), is derived from a^2t^2 + b^2t^2, while the second group, -c(a^2 + b^2), comes from -cb^2 - ca^2. The solution confirms the correctness of the factoring process. Additional factoring topics are expected to be discussed in the coming days.
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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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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
 
More factoring coming in the next few days.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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