Дана функция f(x)=10x2+4x−19.

Вычисли f(−1)=

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+3))(3x+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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