Solve the following problems:
1.) What is the perimeter of a square whose side length is represented by 3x² - 14x + 16?
2.) Add the sum of 4y² + 15y + 9 and -3y² - 12 to the sum of - 8y + 24 and -15y²+ 6y + 4.
3.) What polynomial must be added to 3m²- 5mn - n² to obtain the polynomial m² + 2mn + 3m²n²- 4n²?
4.) What must be subtracted from 12k⁴ + 8k³ + 9k² - 12 to produce 8k⁴ + 8k³ + 25k² - 18k - 16?
5.) Subtract 8p³ + 6p² + p from 12p³ - 10p² + 16 and add the difference to 7p + 4.
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Answer:
1.) Perimeter = 4(3x² - 14x + 16) = 12x² - 56x + 64
2.) 4y² + 15y + 9 + -3y² - 12 + -8y + 24 + -15y²+ 6y + 4 = -16y² + 17y + 37
3.) m² + 2mn + 3m²n² - 4n² + 3m² - 5mn - n² = 4m² + -3mn + 3m²n² - 4n²
4.) 12k⁴ + 8k³ + 9k² - 12 - (8k⁴ + 8k³ + 25k² - 18k - 16) = 4k² - 10k - 28
5.) (12p³ - 10p² + 16) - (8p³ + 6p² + p) + (7p + 4) = 7p² + 8p + 20