Ответы на вопрос:
1) a) 25 - 36p²c² = 5² - (6pc)² = (5 - 6pc)(5+6pc) б) 100a⁴b²c² - 121 = (10a²bc)² - 11² = (10a²bc - 11)(10a²bc +11) 2) а) (3x+1)² - (4x+3)² = (3x+1 -(4x++1+4x+3) = = (3x+ 1 - 4x - 3)(7x + 4) = (-x - 2)(7x+4) = = -(x+2)(7x+4) б) (а+b+c)² - (a -b -c)² = (a+b+c -(a-b-c) ) * (a+b+c +a-b-c) = = (a+b+c -a+b+c) * 2a = (2b + 2c) * 2a = 2(b+c) * 2a = = 4a(b+c) 3) a) x²ⁿ - 9 = (xⁿ)² - 3² = (xⁿ - 3)(xⁿ + 3) б) k² - a⁴ⁿ = k² - (a²ⁿ)² = (k - a²ⁿ)(k + a²ⁿ) в) х²ⁿ - у²ⁿ = (хⁿ -уⁿ)(хⁿ +уⁿ) г)81а⁴ⁿ - 1 = (9а²ⁿ)² - 1² = (9а²ⁿ - 1)(9а²ⁿ + 1) = = ( (3аⁿ)² - 1²)(9а²ⁿ + 1) = (3аⁿ -1)(3аⁿ +1)(9а²ⁿ + 1) 4) а) 2а(5а + 10) + (2а - 8)(3а+2) = = 10а² + 20а + 6а² + 4а - 24а - 16 = = 16а² - 16 = 16(а² - 1) = = 16(а-1)(а+1) б)(3х + 5)(4х - 5) - 2х(2,5 + 1,5х) = = 12х² - 15х + 20х - 25 - 5х - 3х² = = 9х² - 25 = (3x)² - 5² = = (3x - 5)(3x+5)
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