Find the Equation with Real Coefficients y=9 , y=-9

$y = 9$ , $y = - 9$

Step 1

Since the roots of an equation are the points where the solution is $0$ , set each root as a factor of the equation that equals $0$ .

$(y - 9) (y - (- 9)) = 0$

Step 2

Simplify.

Expand $(y - 9) (y + 9)$ using the FOIL Method.

Apply the distributive property.

$y (y + 9) - 9 (y + 9) = 0$

Apply the distributive property.

$y \cdot y + y \cdot 9 - 9 (y + 9) = 0$

Apply the distributive property.

$y \cdot y + y \cdot 9 - 9 y - 9 \cdot 9 = 0$

Simplify terms.

Combine the opposite terms in $y \cdot y + y \cdot 9 - 9 y - 9 \cdot 9$ .

Reorder the factors in the terms $y \cdot 9$ and $- 9 y$ .

$y \cdot y + 9 y - 9 y - 9 \cdot 9 = 0$

Subtract $9 y$ from $9 y$ .

$y \cdot y + 0 - 9 \cdot 9 = 0$

Add $y \cdot y$ and $0$ .

$y \cdot y - 9 \cdot 9 = 0$

Simplify each term.

Multiply $y$ by $y$ .

$y^{2} - 9 \cdot 9 = 0$

Multiply $- 9$ by $9$ .

$y^{2} - 81 = 0$