Question

Factor the perfect square trinomial 16y2 - 24y + 9.

Answer 1

,,Given The expression below

`16y^2-24y+9`

To Factor the given perfect square trinomial

`\begin{gathered} product=9*16y^2=144y^2 \\ sum=-24y \end{gathered}`

Substitute the the sum with two factors of the product

The factors to replace the sum are

`\begin{gathered} -12y*-12y=144y^2 \\ -12y-12y=-24y \end{gathered}`

Replace the sum with the factors

`\begin{gathered} 16y^2-12y-12y+9 \\ 4y(4y-3)-3(4y-3) \\ (4y-3)(4y-3) \end{gathered}`

Hence

16y²-24y+9 = (4y-3)(4y-3) = (4y-3)²