Math Problem Statement
2(x+2)(x-3), expand and complete the square
Solution
Let's first expand the expression .
Step 1: Expand the expression
We can start by expanding using the distributive property (FOIL method):
Now, multiply this result by 2:
So, the expanded expression is:
Step 2: Complete the square
To complete the square for the quadratic expression , we need to follow these steps:
- Factor out the coefficient of (which is 2) from the first two terms:
- Complete the square inside the parentheses. To do this, take the coefficient of (which is -1), divide it by 2, and square it:
So, we add and subtract inside the parentheses:
- Simplify the expression inside the parentheses:
- Distribute the 2:
- Simplify the constants:
So, the expression in completed square form is:
Would you like more details or have any questions on this?
Here are some related questions you might find interesting:
- How do you complete the square for expressions that aren't factored?
- What is the vertex form of a quadratic equation?
- Can completing the square help in solving quadratic equations? If so, how?
- How does completing the square relate to the quadratic formula?
- What is the significance of the completed square form in graphing parabolas?
Tip: When completing the square, always remember to add and subtract the same value inside the parentheses to keep the expression equivalent.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Expressions
Expanding Expressions
Completing the Square
Formulas
(a+b)(a+c) = a^2 + ac + bc + bc
Completing the square method: (x + b/2)^2 - (b/2)^2
Theorems
Distributive Property (FOIL method)
Completing the Square Theorem
Suitable Grade Level
Grades 9-11