(x%2By-z)-(3x%2B2)-(x%2By-1)(3x%2B2).jpeg "(3x+2)(x+y-z)-(3x+2)-(x+y-1)(3x+2)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
In this article, we will simplify the algebraic expression (3x+2)(x+y-z)-(3x+2)-(x+y-1)(3x+2). This expression may seem complex, but with the right steps, we can break it down and simplify it.
Step 1: Expand the Expression
Let's start by expanding the expression using the distributive property.
(3x+2)(x+y-z) = 3x(x+y-z) + 2(x+y-z)
Expanding the expression, we get:
3x(x+y-z) = 3x^2 + 3xy - 3xz
2(x+y-z) = 2x + 2y - 2z
Combining the two expressions, we get:
(3x+2)(x+y-z) = 3x^2 + 3xy - 3xz + 2x + 2y - 2z
Step 2: Simplify the Expression
Now, let's simplify the expression by combining like terms.
(3x+2)(x+y-z) = 3x^2 + 3xy - 3xz + 2x + 2y - 2z
Subtracting (3x+2) from the expression, we get:
(3x+2)(x+y-z) - (3x+2) = 3x^2 + 3xy - 3xz + 2x + 2y - 2z - 3x - 2
Simplifying further, we get:
3x^2 + 3xy - 3xz - x + 2y - 2z - 2
Step 3: Simplify the Remaining Expression
Now, let's simplify the remaining expression (x+y-1)(3x+2).
(x+y-1)(3x+2) = 3x^2 + 3y - 3 + 2x + 2y - 2
Subtracting this expression from the previous result, we get:
3x^2 + 3xy - 3xz - x + 2y - 2z - 2 - (3x^2 + 3y - 3 + 2x + 2y - 2)
Simplifying the expression, we get:
-3xz - x - 3 + z
Final Answer
The simplified expression is:
-3xz - x - 3 + z
In this article, we have successfully simplified the algebraic expression (3x+2)(x+y-z)-(3x+2)-(x+y-1)(3x+2) step-by-step. By breaking down the expression and combining like terms, we were able to simplify the expression to -3xz - x - 3 + z.
