✏️PST
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[tex] \large \bold{\blue{PROBLEM:}} [/tex] Determine the middle term of the following trinomials to make it a perfect square.
- [tex] 100a^2 + \_\_\_ + 1 [/tex]
[tex] \large \bold{\blue{SOLUTION:}} [/tex] To determine the middle term, refer s, t, and u as the first, middle, and last term in PST respectively. "Twice the product of roots of the first and last term is the middle term"
- [tex] t = 2\sqrt{s}\sqrt{u} [/tex]
- [tex] t = 2\sqrt{100a^2}\sqrt{1} [/tex]
- [tex] t = 2(10a)(1) [/tex]
[tex] \large \therefore \underline{\boxed{\tt 100a^2 + \underline{\,\purple{20a}\,} + 1 }} [/tex]
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