Question

drag the tiles to the boxes to form correct pairs. match each trinomial to its factored form. 3y² - 2y - 8, 3y² - 13y - 10, 3y² + 13y - 10, 3y² + 2y - 8, (y - 5)(3y + 2), (y + 5)(3y - 2), (y - 2)(3y + 4), (y + 2)(3y - 4)

Explanation:

Step1: Expand factored - forms

For \((y - 2)(3y + 4)\), use FOIL method: \(y\times3y+y\times4-2\times3y - 2\times4=3y^{2}+4y-6y - 8=3y^{2}-2y - 8\).

Step2: Expand another factored - form

For \((y - 5)(3y + 2)\), use FOIL method: \(y\times3y+y\times2-5\times3y-5\times2 = 3y^{2}+2y-15y - 10=3y^{2}-13y - 10\).

Step3: Expand the third factored - form

For \((y + 5)(3y - 2)\), use FOIL method: \(y\times3y+y\times(-2)+5\times3y+5\times(-2)=3y^{2}-2y + 15y-10=3y^{2}+13y - 10\).

Step4: Expand the fourth factored - form

For \((y + 2)(3y - 4)\), use FOIL method: \(y\times3y+y\times(-4)+2\times3y+2\times(-4)=3y^{2}-4y + 6y-8=3y^{2}+2y - 8\).

Answer:

\(3y^{2}-2y - 8\) matches \((y - 2)(3y + 4)\)
\(3y^{2}-13y - 10\) matches \((y - 5)(3y + 2)\)
\(3y^{2}+13y - 10\) matches \((y + 5)(3y - 2)\)
\(3y^{2}+2y - 8\) matches \((y + 2)(3y - 4)\)