(x%2By-z)-simplify-class-8.jpeg "(x+y+z)(x+y-z) Simplify Class 8")
Simplifying (x+y+z)(x+y-z)
This expression is a product of two binomials. We can simplify it using the distributive property and a little bit of pattern recognition. Here's how:
1. The Distributive Property
The distributive property states that a(b+c) = ab + ac. We can apply this to our expression:
- (x+y+z)(x+y-z) = (x+y+z) * x + (x+y+z) * y + (x+y+z) * (-z)
2. Expanding the Products
Now, let's multiply each term within the parentheses:
- (x+y+z) * x = x² + xy + xz
- (x+y+z) * y = xy + y² + yz
- (x+y+z) * (-z) = -xz - yz - z²
3. Combining Like Terms
Let's add all the terms together and group the like terms:
- x² + xy + xz + xy + y² + yz - xz - yz - z²
- x² + y² - z² + 2xy
Therefore, the simplified form of (x+y+z)(x+y-z) is x² + y² - z² + 2xy.
Key Points:
- Pattern Recognition: Notice that the terms "xz" and "yz" cancel out. This is a common pattern when multiplying binomials with a similar structure.
- Squaring: The simplified form includes the squares of x, y, and z.
- Cross-Multiplication: The term 2xy comes from the cross-multiplication of the terms in the original binomials.
Practice:
To solidify your understanding, try simplifying similar expressions like:
- (a+b+c)(a+b-c)
- (2x+y-3)(2x+y+3)
- (p-q+r)(p-q-r)
Remember to apply the distributive property, expand the products, and combine like terms!