1)
81 - 64x²y² = - ( (8xy)² - 9² ) = - (8xy - 9)(8xy + 9)
144a⁴c²x² - 225 = (12a²cx)² - 15² = (12a²cx - 15)(12a²cx + 15)=
= 3(4a²cx - 5) * 3(4a²cx + 5) = 9(4a²cx - 5)(4a²cx + 5)
2)
(2a+7b)² - (3a - 5b)² = (2a + 7b - (3a-5b))(2a+7b + 3a-5b) =
= (2a + 7b - 3a + 5b)(5a + 2b) = (- a + 12b)(5a + 2b) =
= - (a - 12b)(5a+2b)
(x + y - a)² - (x - y - a )² = (x +y - a - (x - y -a) )(x +y -a +x -y -a )=
= (x +y -a -x +y +a)(2x - 2a) = 2y * 2(x - a) = 4y(x - a )
3)
a²ⁿ - 1 = (aⁿ)² - 1² = (aⁿ - 1)(aⁿ + 1)
x² - y⁴ⁿ = x² - (y²ⁿ)² = (x - y²ⁿ)(x+y²ⁿ )
a⁴ⁿ - b⁴ⁿ = (a²ⁿ)² - (b²ⁿ)² = (a²ⁿ - b²ⁿ)(a²ⁿ + b²ⁿ) =
= ( (aⁿ)² - (bⁿ)² )(a²ⁿ + b²ⁿ) = (aⁿ - bⁿ)(aⁿ + bⁿ )(a²ⁿ + b²ⁿ )
49x⁴ⁿ - 25 = (7x²ⁿ)² - 5² = ( 7x²ⁿ - 5)(7x²ⁿ + 5)
4)
x(3x -19) + (3x - 4)(2x + 9) = 3x² - 19x + 6x² +27x - 8x - 36 =
= (3x² + 6x²) + ( - 19x + 27x - 8x) - 36 = 9x² - 36 =
= 9(x² - 4) = 9(x² - 2²) = 9(x-2)(x+2)
(5a - 4)(3a + 4) - 4a(3.5a + 2) = 15a² +20a - 12a - 16 - 14a² - 8a=
= (15a² - 14a²) + (20a - 12a - 8a) - 16 = a² - 16 =
= a² - 4² = (a - 4)(a + 4)