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PROBLEM
Simplify each expression. (show your solution)
ADDITION OF POLYNOMIALS
1. (4m⁴ - m²) + (5m² + m⁴)
= 4m⁴ - m² + 5m² + m⁴
= 4m⁴ + 4m² + m⁴
= 4m⁴ + m⁴ + 4m²
= 5m⁴ + 4m²
2. (12y² + 17y - 4) + (9y² - 13y + 3)
= 12y² + 17y - 4 + 9y² - 13y + 3
= 12y² + 9y² + 17y - 13y - 4 + 3
= 12y² + 9y² + 17y - 13y - 1
= 21y² + 17y - 13y - 1
= 21y² + 4y - 1
SUBTRACTION OF POLYNOMIALS
3. (5x + x⁴) - (3x⁴ + 4x)
= 5x + x⁴ - (3x⁴ + 4x)
= 5x + x⁴ - 3x⁴ - 4x
= 5x - 2x⁴ - 4x
= -2x⁴ + 5x - 4x
= -2x⁴ + x
4. (5x² - 2x - 1) - (3x² - 5x + 7)
= 5x² - 2x - 1 - (3x² - 5x + 7)
= 5x² - 2x - 1 - 3x² + 5x - 7
= 5x² - 3x² - 2x + 5x - 1 - 7
= 5x² - 3x² - 2x + 5x - 8
= 2x² - 2x + 5x - 8
= 2x² + 3x - 8