36(x+3)^2-x^2 ac^2-bc^2-bc+ac-a+b 3x^2+10x-8

Question

36(x+3)^2-x^2
ac^2-bc^2-bc+ac-a+b
3x^2+10x-8

Answer 1

36 (х + 3)² - х² = (6(x + 3))² - x² = (6x + 18)² - x² = (6x + 18 - x)(6x + 18 + x) = (5x + 18)(7x + 18)
ас² - bc² - bc + ac - a + b = c² (a - b) - c (a - b) - (a - b) = (c² - c - 1)(a - b)
3x² + 10x - 8 = 3 (x - 2/3)(x + 4) = (3x - 2)(x + 4)

3x² + 10x - 8 = 0
D = 10² - 4 * 3 * (- 8) = 196
x₁ = (- 10 + √196) : (2 * 3) = 2/3
x₂ = (- 10 - √196) : (2 * 3) = - 4

Answer 2

1) 36(x+3)²-x²=36(x²+6x+9)-x²=36x²+216x+324-x²=35²+216x+324
2) ac²-bc²-bc+ac-a+b=(ac²+ac)-(bc²+bc)-(a-b)=ac(c+1)-bc(c+1)-(a-b)=
=(c+1) · c(a-b)-(a-b)=(c+1)(a-b)(c-1)
3) 3x²+10x-8
3x²+10x-8=0
D=10²-4 · 3 · (-8)=100+96=196
x₁=(-10+14)/6=2/3
x₂=(-10-14)/6=-4
3x²+10x-8=(x-2/3)(x+4)