\(c)\)

\(a^3+b^3+c^3-3abc\)

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

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

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

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

\(d)\)

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

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

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

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

\(=3\left(a+b\right)\left(ab+ac+bc+c^2\right)\)

\(=3\left(a+b\right)[a\left(b+c\right)+c\left(b+c\right)]\)

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

a)  (-(c-b+a)^2)(4c^2z-8bcz+8acz+4b^2z-8abz+4a^2z-2cy+2by-2ay-3x)

b, (x-2)^2(x-1)

a,

\(x^2+5x+6=x^2+2x+3x+6=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)

b,

\(3x^2-7x+2=3x^2-x-6x+2=x\left(3x-1\right)-2\left(3x-1\right)=\left(3x-1\right)\left(x-2\right)\)

c,

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

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

=)

a) \(x^2+5x+6\)

\(=x^2+2x+3x+6\)

\(=x\left(x+2\right)+3\left(x+2\right)\)

\(=\left(x+3\right)\left(x+2\right)\)

b) \(3x^2-7x+2\)

\(=3x^2-x-6x+2\)

\(=x\left(3x-1\right)-2\left(3x-1\right)\)

\(=\left(x-2\right)\left(3x-1\right)\)

c) Phân tích thành nhân tử $a^3 + b^3 + c^3 - 3abc$ - Đại số - Diễn đàn Toán học

\(=a^3+b^3+c^3+3\left(a+b\right)\left(b+c\right)\left(c+a\right)-4\left(a^3+b^3+c^3\right)-12abc\)

\(=-3\left(a^3+b^3+c^3\right)+3\left(a+b\right)\left(b+c\right)\left(c+a\right)-12abc\)

\(=-3\left(\left(a^3+b^3+c^3\right)-\left(a+b\right)\left(b+c\right)\left(c+a\right)+4abc\right)\)

XONG NHAAAAA :3333333

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

tách ra như bth ấy

Câu 1 :

a) \(x^3-5x^2-14x\)

\(=x^3-7x^2+2x^2-14x\)

\(=x^2\left(x-7\right)+2x\left(x-7\right)\)

\(=\left(x-7\right)\left(x^2+2x\right)\)

\(=x\left(x-7\right)\left(x+2\right)\)

b) \(a^4+a^2+1\)

\(=\left(a^2\right)^2+2a^2+1-a^2\)

\(=\left(a^2+1\right)-a^2\)

\(=\left(a^2-a+1\right)\left(a^2+a+1\right)\)

c) \(x^4+64\)

\(=\left(x^2\right)^2+2\cdot x^2\cdot8+8^2-2\cdot x^2\cdot8\)

\(=\left(x^2+8\right)^2-\left(4x\right)^2\)

\(=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\)

Câu 2 :

a) \(\left(a-b\right)^2=a^2-2ab+b^2\)

Ta có : \(\left(a+b\right)^2=a^2+2ab+b^2\)

\(\Rightarrow a^2+b^2=\left(a+b\right)^2-2ab=7^2-2\cdot14=25\)

\(\Rightarrow\left(a-b\right)^2=25-2\cdot12=1\)

b) tương tự

helpppppp

Ta có: \(A=a^2+ab+2b-4\)

\(\Leftrightarrow\left(a.a\right)+\left(a0+b\right)+\left(20+b\right)-4\)

\(B=x^3-4x^2-8x+8\)

\(\Leftrightarrow\left(x.x.x\right)-\left(40+x\right)^2-\left(80+x\right)+8\)

\(C=x^2-y^2+2yz-z^2\)

\(\Leftrightarrow\left(x.x\right)-\left(y.y\right)+\left(200+y0+z\right)-\left(z.z\right)\)

\(D=5x^3-10x^2+5x\)

\(\Leftrightarrow\left(50.50.50+x.x.x\right)-\left(100+x\right)^2+\left(50+x\right)\)

a) 12x³ + 4x² + 9x + 3 = 4x²(3x + 1) + 3(3x + 1) = (4x² + 3)(3x + 1)

b) x³ + 2x² - x - 2 = x²(x + 2) - (x + 2) = (x² - 1(x + 2) = (x - 1)(x + 1)(x + 2)

c) a³ + (a - b)³ = (a + a - b)[a² - a(a - b) + (a - b)²] = (2a - b)(a² - a² + ab +  a² - 2ab + b²)

= (2a - b)(a² - ab + b²)

a) 12x³ + 4x² + 9x + 3

= 4x²(3x + 1) + 3(3x + 1)

= (4x² + 3)(3x + 1)

b) x³ + 2x² - x - 2

= x²(x + 2) - (x + 2)

= (x² - 1)(x + 2)

c) a³ + (a - b)³ 

= a³ - a²(a - b) + a(a - b)² + (a - b)a² - (a - b)²a + (a - b)³

= a[(a² - a(a - b) + (a - b)²] + (a - b)[a² - a(a - b) + (a - b)²]

= (a + a - b)[(a² - a(a - b) + (a - b)²]