MHB Should I Square Both Trinomials in This Factoring Problem?

[mathdad]

Factor

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

Must I square both trinomials as step 1?

 

[MarkFL]

No, you are given a difference of squares...:D

 

[mathdad]

Let x = (5a^2 - 11a + 10)

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

x^2 - y^2

(x - y)(x + y)

Back-substitute next, correct?

 

[MarkFL]

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

 

[mathdad]

I am learning a lot thanks to you and this website.