10. 4m⁵ - 4m⁴ + 5m⁵
11. 5x - 3x³ + x⁴ - 4x
12. (5 + 7x³ + 3x²) + (- 12 + 5x + 6x²)
= 8x³ + 3x² + 5x + 6x² - 12 - 2x²
= 20x² - 4x
13. (4 + 3x² + 8x³) + (- 7x³ + 12x³ + 6x²)
(4 + 3x² + 8x³) + (- 7x³ + 12x³ + 6x²) = 16x⁴ - 7x³ + 9x²
10. To solve this problem, first simplify the expression by combining like terms:
(4m⁴ - m²) + (5m² + m⁴)
4m⁴ - m² + 5m² + m⁴
Then, factor the expression:
(m⁴ + 5m²) + (4m² - 1)
Now, rewrite the expression as two separate quadratic equations and find the solutions:
m⁴ + 5m² = 0
m²(m² + 5) = 0
11. To solve the problem
(5x + x⁴) - (3x⁴ + 4x)
Step 1: Simplify the terms using the distribution properties of the addition and subtraction
5x + x⁴ = 5x - x³ + x⁴
Step 2: Simplify further using the distribution and substitution properties of addition and subtraction
(5x - x³) + (x⁴ - 4x)
Step 3: Simplify further using the distribution and substitution properties of addition and subtraction
5x - 3x³ + x⁴ - 4x
12. To solve the problem
(5 + 7x³ + 3x²) + (- 12 + 5x + 6x²)
Step 1: Simplify the terms using the distribution and substitution properties of addition and subtraction.
(8x³ + 3x²) + (- 12 + 5x + 6x²)
Step 2: Combine terms where the terms have similar powers.
8x³ + 3x² + 5x + 6x² - 12 - 2x²
Step 3: Simplify further using the distribution and substitution properties of addition and subtraction.
20x² - 4x
13. To solve the problem
(4 + 3x² + 8x³) + (- 7x³ + 12x³ + 6x²)
(12x³ + 3x²) + (- 7x³ + 12x³ + 6x²)
(12x³ + 12x³ - 7x³) + (3x² + 6x²)
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Answers & Comments
10. 4m⁵ - 4m⁴ + 5m⁵
11. 5x - 3x³ + x⁴ - 4x
12. (5 + 7x³ + 3x²) + (- 12 + 5x + 6x²)
= 8x³ + 3x² + 5x + 6x² - 12 - 2x²
= 20x² - 4x
13. (4 + 3x² + 8x³) + (- 7x³ + 12x³ + 6x²)
(4 + 3x² + 8x³) + (- 7x³ + 12x³ + 6x²) = 16x⁴ - 7x³ + 9x²
10. To solve this problem, first simplify the expression by combining like terms:
(4m⁴ - m²) + (5m² + m⁴)
4m⁴ - m² + 5m² + m⁴
Then, factor the expression:
(m⁴ + 5m²) + (4m² - 1)
Now, rewrite the expression as two separate quadratic equations and find the solutions:
m⁴ + 5m² = 0
m²(m² + 5) = 0
11. To solve the problem
(5x + x⁴) - (3x⁴ + 4x)
Step 1: Simplify the terms using the distribution properties of the addition and subtraction
5x + x⁴ = 5x - x³ + x⁴
Step 2: Simplify further using the distribution and substitution properties of addition and subtraction
(5x - x³) + (x⁴ - 4x)
Step 3: Simplify further using the distribution and substitution properties of addition and subtraction
5x - 3x³ + x⁴ - 4x
12. To solve the problem
(5 + 7x³ + 3x²) + (- 12 + 5x + 6x²)
Step 1: Simplify the terms using the distribution and substitution properties of addition and subtraction.
(8x³ + 3x²) + (- 12 + 5x + 6x²)
Step 2: Combine terms where the terms have similar powers.
8x³ + 3x² + 5x + 6x² - 12 - 2x²
Step 3: Simplify further using the distribution and substitution properties of addition and subtraction.
20x² - 4x
13. To solve the problem
(4 + 3x² + 8x³) + (- 7x³ + 12x³ + 6x²)
Step 1: Simplify the terms using the distribution and substitution properties of addition and subtraction.
(12x³ + 3x²) + (- 7x³ + 12x³ + 6x²)
Step 2: Combine terms where the terms have similar powers.
(12x³ + 12x³ - 7x³) + (3x² + 6x²)