Determine the middle term of the following trinomials to make it a perfect square.

9x²+__+16y²

[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{9x^2}\sqrt{16y^2} [/tex]

[tex] t = 2(3x)(4y) [/tex]

[tex] t = 24xy [/tex]

[tex] \large \therefore \underline{\boxed{\tt 9x^2 + \underline{\,\purple{24xy}\,} + 16y^2 }} [/tex]

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UK2019viz UK2019viz · Answer 2

✏️PERFECT SQUARE TRINOMIAL

[tex]\large \bold{\red{DIRECTION:}}[/tex]Determine the middle term of the following trinomials to make it a perfect square.

9x² + __ + 16y²

- If the first and last terms are perfect squares, and the middle term's coefficient is twice the product of the square roots of the first and last terms.

[tex]\sf{{2\sqrt 9x² \: \sqrt 16y²}}[/tex]

[tex] \sf{{2(3x) (4y)}} [/tex]

[tex]\sf{{2(12xy)}} [/tex]

[tex]\sf{{24xy}} [/tex]

[tex]\large \underline{\boxed {\tt \blue{Therefore \: the \: answer \: is \: {\green{24xy}}}}}[/tex]

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