d

\(x^4+2x^3-4x-4\)

\(=\left(x^4+2x^3+x^2\right)-\left(x^2+4x+4\right)\)

\(=\left(x^2+x\right)^2-\left(x+2\right)^2\)

\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)

d: \(=\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)

\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)

e: \(=27x^3-9x^2-18x^2+6x+12x-4\)

\(=\left(3x-1\right)\left(x^2-6x+4\right)\)

Bài giải:

a) x³ + $\frac{1}{27}$ = x³ + ($\frac{1}{3}$)³ = (x + $\frac{1}{3}$)(x² – x . $\frac{1}{3}$+ ($\frac{1}{3}$)²)

=(x + $\frac{1}{3}$)(x² – $\frac{1}{3}$x + $\frac{1}{9}$)

b) (a + b)³ – (a - b)³

= [(a + b) – (a – b)][(a + b)² + (a + b) . (a – b) + (a – b)²]

= (a + b – a + b)(a² + 2ab + b² + a² – b² + a² – 2ab + b²)

= 2b . (3a³ + b²)

c) (a + b)³ + (a – b)³ = [(a + b) + (a – b)][(a + b)² – (a + b)(a – b) + (a – b)²]

= (a + b + a – b)(a² + 2ab + b² – a² +b² + a² – 2ab + b²]

= 2a . (a² + 3b²)

d) 8x³ + 12x²y + 6xy² + y³ = (2x)³ + 3 . (2x)² . y +3 . 2x . y + y³ = (2x + y)³

e) - x³ + 9x² – 27x + 27 = 27 – 27x + 9x² – x³ = 3³ – 3 . 3² . x + 3 . 3 . x² – x³ = (3 – x)³

WOW !!! Tốc độ đánh máy của bạn thần thánh thật đấy......2 phút mà nhiều quá trời luôn

a)4y(x-1)-(x+1)=4y(x-1)-(X-1)

   =(x-1) (4y-1)

b)\(\left(x-3\right)^3\)+3-x=(x-3)^3+(x-3)

=x-3 (x-3)^2

HOK TỐT K NHA

a) \(a^3\left(b-c\right)+b^3\left(c-a\right)+c^3\left(a-b\right)\)

\(=a^3b-a^3c+b^3\left(c-a\right)+c^3a-c^3b\)

\(=\left(a^3b-c^3b\right)+\left(c^3a-a^3c\right)+b^3\left(c-a\right)\)

\(=-b\left(c^3-a^3\right)+ca\left(c^2-a^2\right)+b^3\left(c-a\right)\)

\(=-b\left(c-a\right)\left(c^2-ac+a^2\right)+ca\left(c+a\right)\left(c-a\right)+b^3\left(c-a\right)\)

\(=\left(c-a\right)\left(-c^2b+abc-a^2b\right)+\left(c-a\right)\left(c^2a+ca^2\right)+b^3\left(c-a\right)\)

\(=\left(c-a\right)\left(-c^2b+abc-a^2b+c^2a+ca^2+b^3\right)\)

a) a³ (b-c) + b³ (c-a) +c³ (a-b)

<=> a³b – a³c +b³c – b³a + c³a – c³b

<=>  b(a³ – c³) +c(a³ – b³) + a(b³ - c³)

(Tự áp dụng hằng đẳng thức)

b)