(x%2B10)-class-9.jpeg "(x+4)(x+10) Class 9")
Expanding (x+4)(x+10): A Class 9 Algebra Lesson
In Class 9, you'll encounter many algebraic expressions, and understanding how to expand them is crucial. One common example is expanding expressions like (x+4)(x+10). Let's break down the steps involved:
Understanding the Concept
This expression represents the multiplication of two binomials, (x+4) and (x+10). To expand it, we need to distribute each term in the first binomial to each term in the second binomial. This is often referred to as the FOIL method, which stands for:
- First terms: x * x = x²
- Outer terms: x * 10 = 10x
- Inner terms: 4 * x = 4x
- Last terms: 4 * 10 = 40
Expanding the Expression
- Multiply the First terms: x * x = x²
- Multiply the Outer terms: x * 10 = 10x
- Multiply the Inner terms: 4 * x = 4x
- Multiply the Last terms: 4 * 10 = 40
Combining Like Terms
Now we have: x² + 10x + 4x + 40
Combining the like terms (10x and 4x): x² + 14x + 40
Final Expanded Form
Therefore, the expanded form of (x+4)(x+10) is x² + 14x + 40.
Why is This Important?
Understanding how to expand binomials is essential for:
- Solving quadratic equations: Expanding binomials helps us rewrite equations into standard quadratic form (ax² + bx + c = 0).
- Simplifying expressions: Many complex algebraic expressions can be simplified by expanding binomials.
- Factorization: Recognizing the expanded form helps us factor expressions back into their binomial form.
Practice Makes Perfect
Practice expanding different binomials to get comfortable with the process. You can start with simple examples and gradually work your way to more complex ones. Remember, the key is to understand the concept of distribution and combine like terms correctly.