1) Add 2x² + 3x + 2 and 3x² - 5x - 1
Just do the simple addition. Make sure to add like terms. For instance: Add 3x² with 2x² only, not with 3x and 2.
→ 2x² + 3x + 2 + 3x² - 5x - 1
→ 2x² + 3x² + 3x - 5x + 2 - 1
→ 5x² - 2x + 1
2) Subtract x² - 4 and 12x² + 4x - 6
The law of subtraction is to subtract the smaller value from the larger value. But it is not necessary that it is always applicable. Its value can be positive, negative and zero (which varies with the given values).
→ x² - 4 - (12x² + 4x - 6)
There will be no change in sign during addition. But if you're doing subtraction change the signs.
→ x² - 4 - 12x² - 4x + 6 [ Product of (-)(-) is (+) and (+)(-) is (-) ]
→ x² - 12x² - 4x - 4 + 6
→ - 11x² - 4x + 2
3) Add 6x² + 3x - 4 and x² - 7
→ 6x² + 3x - 4 + x² - 7
→ 6x² + x² + 3x - 4 - 7
→ 7x² + 3x - 11
4) Add 7x³ + 4x - 1 and 2x² - 6x + 2
→ 7x³ + 4x - 1 + 2x² - 6x + 2
→ 7x³ + 2x² + 4x - 6x - 1 + 2
→ 7x³ + 2x² - 2x + 1
5) Subtract 5x⁴ - 4x³ - 3x - 4 and -2x⁴ - 6x³ + 2x
→ 5x⁴ - 4x³ - 3x - 4 - (-2x⁴ - 6x³ + 2x)
→ 5x⁴ - 4x³ - 3x - 4 + 2x⁴ + 6x³ - 2x
→ 5x⁴ + 2x⁴ - 4x³ + 6x³ - 3x - 2x - 4
→ 7x⁴ + 2x³ - 5x - 4