Представьте в виде произведения трёх множителей: 16 – x4. a2(b – 1) – b+1. a4

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Представьте в виде произведения трёх множителей: 16 – x4. a2(b – 1) – b+1. a4 – 1. b(x2 – 4) + 4 – x2. 9a3 – 9a2b – a +b. y3 – 5y2 – 16y+ 80.

Answers & Comments

kolobok1431 Везде применяется формула разности квадратов:
a² - b² = (a-b)(a+b)
1.
16 – x⁴ = (4² - x²)² = (4-x²)(4+x²) = (2²-x²)(4+x²) = (x-2)(x+2)(4+x²)
2.
a²(b – 1) – b+1 = а²(b-1) - (b-1) = (b-1)(a² - 1) = (b-1)(a-1)(a+1)
3.
a⁴ – 1 = (a²)² - 1² = (a²-1²)(a²+1) = (a-1)(a+1)(a²+1)
4.
b(x² – 4) + 4 – x² = b(x²-4) - (x² - 4) = (x² - 4)(b-1) = (x² - 2²)(b - 1) =
= (x-2)(x+2)(b-1)
5.
9a³ – 9a²b – a + b = (9a³ – 9a²b) – (a - b) = 9a²(a-b) - (a - b) =
= (a-b)(9a² - 1) = (a-b)(3a -1)(3a + 1)
6.
y³ – 5y² – 16y+ 80 = (y³ – 5y²) – (16y- 80) = y²(y-5) - 16(y-5) =
= (y-5)(y² - 16) = (y-5)(y² - 4²) = (y-5)(y-4)(y+4).

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