MHB Should I Square Both Trinomials in This Factoring Problem?

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To factor the expression (5a^2 - 11a + 10)^2 - (4a^2 - 15a + 6)^2, it is not necessary to square both trinomials initially since it represents a difference of squares. By letting x = (5a^2 - 11a + 10) and y = (4a^2 - 15a + 6), the expression can be rewritten as x^2 - y^2. This can be factored using the formula (x - y)(x + y). After factoring, the next step involves back-substituting and combining like terms for simplification.
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Factor

(5a^2 - 11a + 10)^2 - (4a^2 - 15a + 6)^2

Must I square both trinomials as step 1?
 
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No, you are given a difference of squares...:D
 
Let x = (5a^2 - 11a + 10)

Let y = (4a^2 - 15a + 6)

x^2 - y^2

(x - y)(x + y)

Back-substitute next, correct?
 
RTCNTC said:
Let x = (5a^2 - 11a + 10)

Let y = (4a^2 - 15a + 6)

x^2 - y^2

(x - y)(x + y)

Back-substitute next, correct?

Yes, then combine like terms. :D
 
I am learning a lot thanks to you and this website.
 

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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