(a%2B2)%3D0-solve-by-factoring.jpeg "(a+1)(a+2)=0 Solve By Factoring")
Solving the Equation (a+1)(a+2)=0 by Factoring
In this article, we will solve the quadratic equation (a+1)(a+2)=0 using the factoring method.
The Given Equation
The given equation is:
(a+1)(a+2)=0
Factoring the Equation
To solve this equation, we will start by factoring the left-hand side of the equation.
(a+1)(a+2) = a(a+2) + 1(a+2)
= a^2 + 2a + a + 2
= a^2 + 3a + 2
Now, we can factor the quadratic expression:
a^2 + 3a + 2 = (a+1)(a+2)
Solving the Factored Equation
Since we have factored the equation, we can now solve for a by setting each factor equal to 0:
(a+1) = 0 or (a+2) = 0
Solving for a
Case 1: (a+1) = 0
Subtracting 1 from both sides gives:
a = -1
Case 2: (a+2) = 0
Subtracting 2 from both sides gives:
a = -2
Conclusion
Therefore, the solutions to the equation (a+1)(a+2)=0 are a = -1 and a = -2.
