Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x^3-7x-6\)
\(=x^3-3x^2+3x^2-9x+2x-6\)
\(=x^2\left(x-3\right)+3x\left(x-3\right)+2\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+3x+2\right)\)
\(=\left(x-3\right)\left(x+1\right)\left(x+2\right)\)
a) -x2 + 2x - 1
= -( x2 - 2x + 1 )
= -( x - 1 )2
b) 12y - 36 - y2
= -( y2 - 12y + 36 )
= -( y - 6 )2
c) -x3 + 9x2 - 27x + 27
= -( x3 - 9x2 + 27x - 27 )
= -( x - 3 )3
d) x3 - 6x2 + 9x
= x( x2 - 6x + 9 )
= x( x - 3 )2
e) a3b - ab3
= ab( a2 - b2 )
= ab( a - b )( a + b )
f) a2 + 2a + 1 - b2
= a2 + ab + a - ab - b2 - b + a + b + 1
= a( a + b + 1 ) - b( a + b + 1 ) + 1( a + b + 1 )
= ( a - b + 1 )( a + b + 1 )
a)\(-x^2+2x-1\)
\(=-\left(x^2-2x+1\right)\)
\(=-\left(x-1\right)^2\)
b) \(12y-36-y^2\)
\(=-\left(y^2-12y+36\right)\)
\(=-\left(y^2-2\cdot1\cdot6+6^2\right)\)
\(=-\left(y-6\right)^2\)
c) \(-x^3+9x^2-27x+27\)
\(=-x^3+3x^2+6x^2-18x-9x+27\)
\(=-x^2\left(x-3\right)+6x\left(x-3\right)-9\left(x-3\right)\)
\(=\left(x-3\right)\left(-x^2+6x-9\right)\)
\(=\left(x-3\right)\cdot-\left(x^2-6x+9\right)\)
\(=\left(x-3\right)\cdot-\left(x^2-2\cdot x\cdot3+3^2\right)\)
\(=-\left(x-3\right)\left(x-3\right)^2\)
\(=\left(x-3\right)^3\)
d) \(x^3-6x^2+9\)
\(=x\left(x^2-6x+9\right)\)
\(=x\left(x-3\right)^2\)
e) \(a^3b-ab^3\)
\(=ab\left(a^2-b^2\right)\)
\(=ab\left(a-b\right)\left(a+b\right)\)
f) \(a^2+2a+1-b^2\)
\(=a^2+2\cdot a\cdot1+1^2-b^2\)
\(=\left(a+1\right)^2-b^2\)
\(=\left(a+1-b\right)\left(a+1+b\right)\)
x3 + 7x - 6=x2 . x + 7x - 22 + 2 = (x2 - 22) + (x+7x)+2=(x-2) . (x+2) + 8x + 2
x3 - 5x + 8x - 4=x2 . x -5x + 8x -22 = (x2 - 22) . (x -5x + 8x )=(x-2) . (x+2) . 4x
x3 - 9x2 + 6x + 16=x2 . x - 9x2 + 6x + 16 = (x2 - 9x2) . (x+6x) + 16=(x-9x) . (x+9x) . 7x + 16
k mk nha
1.
2x3-x2+5x+3=2x3+x2-2x2-x+6x+3=(2x+1)(x2-x+3)
2.
(x+2)(x+3)(x+4)(x+5)-24=(x2+7x+10)(x2+7x+12)-24
Đặt x2+7x+11=a
Ta cso:
(a-1)(a+1)-24=a2-1-24=a2-25=(a-5)(a+5)=(x2+7x+6)(x2+7x+16)
3.
27x3-27x2+18x-4=27x3-9x2-18x2+6x+12x-4=(3x-1)(9x2-6x+4)
\(\text{1) }2x^3-x^2+5x+3\\ =2x^3-2x^2+x^2+6x-x+3\\ =\left(2x^3-2x^2+6x\right)+\left(x^2-x+3\right)\\ =2x\left(x^2-x+3\right)+\left(x^2-x+3\right)\\ =\left(2x+1\right)\left(x^2-x+3\right)\\ \)
\(\text{2) }\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\\ =\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]-24\\ =\left(x^2+2x+5x+10\right)\left(x^2+3x+4x+12\right)-24\\ =\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\left(1\right)\\ \text{Đặt }x^2+7x+11=y\text{ }\text{ }\left(\text{*}\right)\\ Thay\text{ }\: \left(\text{*}\right)\text{ vào }\left(1\right)\\ \text{ }Ta\text{ }đư\text{ợc }:\\ \left(1\right)=\left(y-1\right)\left(y+1\right)-24\\ =y^2-1-24\\ =y^2-25\\ =\left(y-5\right)\left(y+5\right)\text{ }\text{ }\left(2\right)\\ Thay\text{ }\left(\text{*}\right)\text{ vào }\left(2\right)\\ \text{Ta lại được: }\left(2\right)=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)\\ =\left(x^2+7x+6\right)\left(x^2+7x+17\right)\\ =\left(x^2+6x+x+6\right)\left(x^2+7x+17\right)\\ =\left[\left(x^2+6x\right)+\left(x+6\right)\right]\left(x^2+7x+17\right)\\ =\left[x\left(x+6\right)+\left(x+6\right)\right]\left(x^2+7x+17\right)\\ =\left(x+1\right)\left(x+6\right)\left(x^2+7x+17\right)\\ \)
\(\text{3) }27x^3-27x^2+18x-4\\ =27x^3-18x^2-9x^2+12x+6x-4\\ =\left(27x^3-18x^2+12x\right)-\left(9x^2-6x+4\right)\\ =3x\left(9x^2-6x+4\right)-\left(9x^2-6x+4\right)\\ =\left(3x-1\right)\left(9x^2-6x+4\right)\\ \)
1: \(=x^3-8x^2-x^2+8x-2x+16\)
\(=\left(x-8\right)\left(x^2-x-2\right)=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)
2: \(=x^3+2x^2-8x^2-16x+15x+30\)
\(=\left(x+2\right)\left(x^2-8x+15\right)\)
\(=\left(x+2\right)\left(x-3\right)\left(x-5\right)\)
3: \(=2x^3+x^2-2x^2-x+6x+3\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
4: \(=64x^4+16x^2y^2+y^4-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2-4xy+y^2\right)\left(8x^2+4xy+y^2\right)\)