2-(a%2B3)(a-3).jpeg "(a-3)2-(a+3)(a-3)")
Simplifying the Expression: (a - 3)² - (a + 3)(a - 3)
This article will guide you through simplifying the expression (a - 3)² - (a + 3)(a - 3). We'll break down the steps and use algebraic properties to reach the most simplified form.
Step 1: Recognizing the Pattern
The expression contains two terms:
- (a - 3)²: This is a squared binomial, which can be expanded using the formula: (x - y)² = x² - 2xy + y²
- (a + 3)(a - 3): This is a product of two binomials in the form (x + y)(x - y), which is a difference of squares and simplifies to x² - y².
Step 2: Expanding the Terms
Let's expand each term based on the recognized patterns:
- (a - 3)² = a² - 2(a)(3) + 3² = a² - 6a + 9
- (a + 3)(a - 3) = a² - 3² = a² - 9
Step 3: Combining the Terms
Now, substitute the expanded terms back into the original expression:
(a - 3)² - (a + 3)(a - 3) = (a² - 6a + 9) - (a² - 9)
Simplify by distributing the negative sign:
= a² - 6a + 9 - a² + 9
Step 4: Simplifying the Expression
Combine like terms:
= -6a + 18
Final Result
Therefore, the simplified form of (a - 3)² - (a + 3)(a - 3) is -6a + 18.