Verified answer

1) y² - 100 = y² - 10² = (y - 10)(y + 10)

2) - 0,16x² + y2 = y² - 0,16x² = y² - (0,4x)² = (y - 0,4x)(y + 0,4x)

3) a⁴ - 25 = (a² )² - 5² = (a² - 5)(a² + 5)

4) 2x² - 12x + 18 = 2(x² - 6x + 9) = 2(x - 3)² = 2(x - 3)(x - 3)

5) 16x + 8x² + x³ = x³ + 8x² + 16x = x(x² + 8x + 16) = x(x + 4)² =

= x(x + 4)(x + 4)

6) x³ - xy² - 6y² + 6x² = (x³ - xy²) - (6y² - 6x²) = x(x² - y²) - 6(x² - y²) = (x² - y²)(x - 6) =

= (x - y)(x + y)(x - 6)

7) 8x⁴y - xy⁴ = xy(8x³ - y³) = xy(2x - y)(4x² + 2xy + y²)

Ответ :    y²-100=(y-10)(y+10)

-o,16x²+y²=(y-0.4)(y+0,4)

3)  ....=  (a²)²-5²=(a²-5)(a²+5)

2x²-12x+18=2·(x²-6x+9)=2(x-3)²

16x+8x²+x³=x(16+8x+x²)=x(4+x)²

x³-xy²-6y²+6x²=x(x²-y²)+6(x²-y²)=(x²-y²)·(x+y)=(x-y)(x+y)(x+y)=(x-y)(x+y)²

7)  ....=xy(8x³-y³)=xy((2x)³-y³)=xy(2x-y)(4x²+2xy+y²)

Объяснение: