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 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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