4. Đặt  t= a^2 +a

Suy ra t^2 +4t - 12 = (t-2)(t+6) = (a^2+a-2) (a^2+a +6) = (a-1)(a+2)(a^2+a+6)

5. Đặt t = x^2 +x+1

Ta có: t(t+1) -12

= t^2 +t-12

= (t-3)(t+4)

= ( x^2 +x -2 ) (x^2+x+5)

 = (x-1) ( x+2) (x^2+x+5)

6. x^8 + x^7 + x^6 - x^7- x^6 - x^5 + x^5+ x^4 + x^3- x^4- x^3- x^2 + x^2 + x +1

= (x^2 +x+1) ( x^6 - x^5 +x^3 -x^2 +1)

7.  x^10 + x^9 +x^8 - x^9- x^8- x^7 +x^7+x^6+x^5 - x^6-x^5 - x^4 + x^5+ x^4 + x^3 - x^3 - x^2 - x + x^2 + x +1

=  (x^2 + x + 1) ( x^8 -x^7 + x^5 - x^4 + x^3 -x + 1)

         a³ - 7a - 6 

= a³ - a - 6a - 6 

= a ( a² - 1 ) - 6 ( a + 1 )

= a ( a - 1 ) ( a + 1 ) - 6 ( a + 1 )

= ( a + 1 ) [ ( a ( a - 1 ) - 6 ]

= ( a + 1 ) ( a² - a - 6  )

= ( a + 1 ) ( a² + 2a - 3a - 6 )

= ( a + 1 ) ( a + 2 ) ( a - 3 )

1. a³ - 7a - 6 

= a^3 - a - 6a - 6

= a(a^2 - 1) - 6(a + 1)

= a(a - 1)(a + 1) - 6(a + 1)

= (a+1)(a^2 - a - 6)

= (a+1)(a^2 -3a + 2a - 6)

= (a+1)[a(a-3) + 2(a-3)]

= (a+1)(a+2)(a-3)

2. a³ + 4a² - 7a - 10

= a^3 + 5a^2 - a^2 - 5a - 2a - 10

= a^2(a+5) - a(a+5) - 2(a + 5)

= (a^2 - a - 2)(a+5)

= (a^2 + a - 2a - 2)(a+5)

= [a(a+1) - 2(a+1)](a+5)

= (a+1)(a-2)(a+5)

 a) 3x2 – 7x + 2

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

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

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

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

 b) a(x2 + 1) – x(a2 + 1)

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

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

.......?

a) Ta có: \(3x^2-7x+2\)

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

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

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

b) Ta có: \(a\left(x^2+1\right)-x\left(a^2+1\right)\)

\(=x^2a+a-a^2x-x\)

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

\(=xa\left(x-a\right)-\left(x-a\right)\)

\(=\left(x-a\right)\left(xa-1\right)\)

c) Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)

\(=\left(x^2+7x\right)^2+16\left(x^2+7x\right)+6\left(x^2+7x\right)+96\)

\(=\left(x^2+7x\right)\left(x^2+7x+16\right)+6\left(x^2+7x+16\right)\)

\(=\left(x^2+7x+16\right)\left(x^2+7x+6\right)\)

\(=\left(x^2+7x+16\right)\left(x+1\right)\left(x+6\right)\)

d) Ta có: \(\left(a+1\right)\left(a+3\right)\left(a+5\right)\left(a+7\right)+15\)

\(=\left(a^2+8a+7\right)\left(a^2+8a+15\right)+15\)

\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+105+15\)

\(=\left(a^2+8a\right)^2+22\left(a^2+8a\right)+120\)

\(=\left(a^2+8a\right)^2+12\left(a^2+8a\right)+10\left(a^2+8a\right)+120\)

\(=\left(a^2+8a\right)\left(a^2+8a+12\right)+10\left(a^2+8a+12\right)\)

\(=\left(a^2+8a+12\right)\left(a^2+8a+10\right)\)

\(=\left(a+2\right)\left(a+6\right)\left(a^2+8a+10\right)\)

\(a,=\left(x+1\right)\left(x+3\right)\\ b,=-5x^2+15x+x-3=\left(x-3\right)\left(1-5x\right)\\ c,=2x^2+2x+5x+5=\left(2x+5\right)\left(x+1\right)\\ d,=2x^2-2x+5x-5=\left(x-1\right)\left(2x+5\right)\\ e,=x^3+x^2-4x^2-4x+x+1=\left(x+1\right)\left(x^2-4x+1\right)\\ f,=x^2+x-5x-5=\left(x+1\right)\left(x-5\right)\)

MK KO BT MK MỚI HO C LỚP 6

AI HỌC LỚP 6 CHO MK XIN

\(a,a^3-7a-6\)

\(\Leftrightarrow a^3+a^2-a^2-a-6a-6\)

\(\Leftrightarrow a^2\left(a+1\right)-a\left(a+1\right)-6\left(a+1\right)\)

\(\Leftrightarrow\left(a+1\right)\left(a^2-a-6\right)\)

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

\(b,a^3+4a^2-7a-10\)

\(\Leftrightarrow a^3+5a^2-a^2-5a-2a-10\)

\(\Leftrightarrow a^2\left(a+5\right)-a\left(a+5\right)-2\left(a+5\right)\)

\(\Leftrightarrow\left(a+5\right)\left(a+1\right)\left(a-2\right)\)

\(d,\left(a^2+a\right)^2+4\left(a^2+a\right)-12\)

Đặt a^2+a=y ta có 

y^2+4y-12=(y+6)(y-2)

<=> (a^2+a+6)(a^2+a-2)

<=> (a^2+a+6)(x-1)(x+2)

a, \(4abc-8ab^2c=4abc\left(1-2b\right)\)

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

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

c, \(9a^4\left(a-2\right)+a^2\left(a-2\right)=a^2\left(9a^2+1\right)\left(a-2\right)\)

d, \(\left(a-4\right)\left(2a-1\right)-8a+4=\left(a-4\right)\left(2a-1\right)-4\left(2a-1\right)\)

\(=\left(a-8\right)\left(2a-1\right)\)

a) `4abc-8ab^2c=4abc(1-2b)`

b) `x^2 (2a-1)+x(1-2a) = x^2 (2a-1) -x(2a-1) = (2a-1)(x^2-x)=x(2a-1)(x-1)`

c) `9a^4 (a-2) +a^2 (a-2) = (a-2)(9a^4+a^2)=a^2 (a-2)(9a^2+1)`

d) `(a-4)(2a-1)-8a+4=(a-4)(2a-1)-4(2a-1)=(2a-1)(a-8)`

1.

$a^3-7a-6=a^3-a-(6a+6)=a(a^2-1)-6(a+1)$

$=a(a-1)(a+1)-6(a+1)=(a+1)(a^2-a-6)$

$=(a+1)(a^2+2a-3a-6)$

$=(a+1)[a(a+2)-3(a+2)]=(a+1)(a+2)(a-3)$

2.

\(a^3+4a^2-7a-10=a^3+a^2+(3a^2+3a)-(10a+10)\)

\(=a^2(a+1)+3a(a+1)-10(a+1)=(a+1)(a^2+3a-10)\)

\(=(a+1)[a(a-2)+5(a-2)]=(a+1)(a-2)(a+5)\)

3.

\(a(b+c)^2+b(c+a)^2+c(a+b)^2-4abc\)

\(=a(b^2+c^2+2bc)+b(c^2+a^2+2ac)+c(a^2+b^2+2ab)-4abc\)

\(=ab(a+b)+bc(b+c)+ca(c+a)+2abc\)

\(=ab(a+b+c)+bc(a+b+c)+ac(a+c)\)

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

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

4.

\((a^2+a)^2+4(a^2+a)-12\)

\(=(a^2+a)^2-2(a^2+a)+6(a^2+a)-12\)

\(=(a^2+a)(a^2+a-2)+6(a^2+a-2)\)

\(=(a^2+a-2)(a^2+a+6)\)

\(=[a(a+2)-(a+2)](a^2+a+6)=(a-1)(a+2)(a^2+a+6)\)