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Simplifying Polynomial Expressions
This article will guide you through simplifying the polynomial expression:
(12x⁵ - 3x⁴ + 2x - 5) + (8x⁴ - 3x³ + 4x + 1)
Understanding the Process
Simplifying polynomial expressions involves combining like terms. Like terms are those with the same variable and exponent.
Key steps:
- Remove the parentheses: Since we are adding the two polynomials, the parentheses don't affect the signs of the terms.
- Identify like terms: Look for terms with the same variable and exponent.
- Combine like terms: Add the coefficients of the like terms.
Simplifying the Expression
-
Remove the parentheses: 12x⁵ - 3x⁴ + 2x - 5 + 8x⁴ - 3x³ + 4x + 1
-
Identify like terms:
- x⁵ terms: 12x⁵
- x⁴ terms: -3x⁴ + 8x⁴
- x³ terms: -3x³
- x terms: 2x + 4x
- Constant terms: -5 + 1
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Combine like terms:
- 12x⁵
- (-3 + 8)x⁴ = 5x⁴
- -3x³
- (2 + 4)x = 6x
- -5 + 1 = -4
The Simplified Expression
The simplified form of the expression is:
12x⁵ + 5x⁴ - 3x³ + 6x - 4