Phân tích đa thức thành nhân tử :
a) ( b - a )^2 + ( a - b )( 3a - 2b ) - a^2 + b^2
b) ( x^2 - 2x + 3 )( x^2 - 2x + 5 ) - 8
c) x^8 + x^7 + 1
Phân tích đa thức thành nhân tử
1/ (a-3b)(a+3b)+(a-4b)(2b+3a)+(3b-a)(2a-b)
2/ (x-2y)(x+2y)+(2y-x)(3y-2x)+(y-x)2
1/Tự chép lại đb nha :v
=a2 - 9b2+2ab+3a2-8b2-12ab+6ab-3b2-2a2+ab
= 2a2-3ab-20b2
= (2a2+5ab) - (8ab+20b2)
= a(2a+5b) - 4b(2a+5b)
=(2a+5b)(a-4b)
câu 2 tương tự nhé :)
Bài 1: Phân tích đa thức thành nhân tử
a. (a+2b).(a-3b)-(2b+a).(3a+b)
b. (x-2)2-(3x+4).(2x-2)
c. 2x4.(3x+5)-32.(3x+5)
d. x2-4+(x-2)2
f. (x2-25)2-4.(x+5)2
Bài 1: Phân tích đa thức thành nhân tử
a) (6x+3)-(2x-5)(2x+1)
b) (3x-2)(4x-3)-(2-3x)(x-1)-2(3x-2)(x+1)
Bài 2*:Phân tích đa thức thành nhân tử
a) (a-b)(a+2b)-(b-a)(2a-b)-(a-b)(a+3b)
b) 5xy3-2xy2-15y2+6z
c) (x+y)(2x-y)+(2x-y)(3x-y)-(y-2x)
d) ab3c2-a2b2c2+ab2c3-a2bc
e) x2(y-z)+y2(z-x)+z2(x-y)
f) x2-6xy+9y2+4x-12y
Bài 1:
a: Ta có: \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)
\(=\left(2x+1\right)\left(3-2x+5\right)\)
\(=\left(2x+1\right)\left(8-2x\right)\)
\(=2\left(4-x\right)\left(2x+1\right)\)
b) Ta có: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)
\(=3\left(3x-2\right)\left(x-2\right)\)
Bài 2:
a: Ta có: \(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)
\(=\left(a-b\right)\left(2a-4b\right)\)
\(=2\left(a-b\right)\left(a-2b\right)\)
f: Ta có: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)
1. Phân tích đa thức thành nhân tử: \(4x^2-17xy+13y^2\)
2. Tìm biết: 2x(x-5)-x(3+2x)=26
3. Tính giá trị biểu thức: \(A=\left(2a-3b\right)^2+2\left(2a-3b\right)\left(3a-2b\right)+\left(2b-3a\right)^2\) biết a-b=10
giúp mị ik
1. \(4x^2-17xy+13y^2=4x^2-4xy-13xy+13y^2=4x\left(x-y\right)-13y\left(x-y\right)=\left(x-y\right)\left(4x-13y\right)\)
2. \(2x\left(x-5\right)-x\left(3+2x\right)=26\Leftrightarrow2x^2-10x-3x-2x^2=26\Leftrightarrow-13x=26\Leftrightarrow x=-2\)
3. \(A=\left(2a-3b\right)^2+2\left(2a-3b\right)\left(3a-2b\right)+\left(2b-3a\right)^2\)
\(\Leftrightarrow\left(2a-3b\right)^2-2\left(2a-3b\right)\left(2b-3a\right)+\left(2b-3a\right)^2=\left(2a-3b-2b+3a\right)^2=\left(5a-5b\right)^2\)
\(=25\left(a-b\right)^2=25\cdot100=2500\)
Phân tích đa thức thành nhân tử
1) 2x^2 - 5XY - 3y^2
2) 7x^2+3xy-10y^2
3)x^2+5x-2
4)x^8+x^7+1
5)x^7+x^5+1
6)x^4+324
7)x^5-5x^3+4x
8)a^2b^2 (a-b) + b^2c^2(b-c) + c^2a^2.(c-a)
Mấy câu dễ mình làm trước nhé. Mấy câu khó hơn mình trình bày sau :)
1) 2x2 - 5xy - 3y2 = 2x2 + xy - 6xy - 3y2 = x( 2x + y ) - 3y( 2x + y ) = ( 2x + y )( x - 3y )
2) 7x2 + 3xy - 10y2 = 7x2 - 7xy + 10xy - 10y2 = 7x( x - y ) + 10y( x - y ) = ( x - y )( 7x + 10y )
3) x2 + 5x - 2 = ( x2 + 5x + 25/4 ) - 33/4 = ( x + 5/2 )2 - \(\left(\frac{\sqrt{33}}{2}\right)^2\)= \(\left(x+\frac{5}{2}-\frac{\sqrt{33}}{2}\right)\left(x+\frac{5}{2}+\frac{\sqrt{33}}{2}\right)\)
6) x4 + 324 = ( x4 + 36x2 + 324 ) - 36x2 = ( x2 + 18 )2 - ( 6x )2 = ( x2 - 6x + 18 )( x2 + 6x + 18 )
4) x8 + x7 + 1
= x8 + x7 + x6 - x6 + 1
= x6( x2 + x + 1 ) - ( x6 - 1 )
= x6( x2 + x + 1 ) - ( x3 - 1 )( x3 + 1 )
= x6( x2 + x + 1 ) - ( x - 1 )( x2 + x + 1 )( x3 + 1 )
= ( x2 + x + 1 )( x6 - ( x - 1 )( x3 + 1 ) ]
= ( x2 + x + 1 )( x6 - x4 + x3 - x + 1 )
5) x7 + x5 + 1
= x7 + x6 - x6 + x5 + 1
= x5( x2 + x + 1 ) - ( x6 - 1 )
= x5( x2 + x + 1 ) - ( x3 - 1 )( x3 + 1 )
= x5( x2 + x + 1 ) - ( x - 1 )( x2 + x + 1 )( x3 + 1 )
= ( x2 + x + 1 )[ x5 - ( x - 1 )( x3 + 1 ) ]
= ( x2 + x + 1 )( x5 - x4 + x3 - x + 1 )
7) x5 - 5x3 + 4x
= x5 - x3 - 4x3 + 4x
= x3( x2 - 1 ) - 4x( x2 - 1 )
= ( x2 - 1 )( x3 - 4x )
= ( x - 1 )( x + 1 )x( x2 - 4 )
= x( x - 1 )( x + 1 )( x - 2 )( x + 2 )
8) Xin hàng :)
Phân tích đa thức sau thành nhân tử
a) (a^2+b^2)^2-4a^2b^2
b) 3x^2-3xy-5x+5y
c) -x^3+3x^2 -3x+1
d) 2x^2+4xy+2y^2- 8z^2
e) a^3-a^2-a+1
f) x^3-2xy-x^2y+2y^2
e) Ta có: \(a^3-a^2-a+1\)
\(=a^2\left(a-1\right)-\left(a-1\right)\)
\(=\left(a-1\right)\left(a^2-1\right)\)
\(=\left(a-1\right)^2\cdot\left(a+1\right)\)
f) Ta có: \(x^3-2xy-x^2y+2y^2\)
\(=x^2\left(x-y\right)-2y\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2-2y\right)\)
a) \(\left(a^2+b^2\right)^2-4a^2b^2=\left(a^2+b^2+2ab\right)\left(a^2+b^2-2ab\right)=\left(a+b\right)^2.\left(a-b\right)^2\)
b) \(3x^2-3xy-5x+5y=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
c) \(-x^3+3x^2-3x+1=\left(1-x\right)^3\)
d) Đề sai ko ???
e) \(a^3-a^2-a+1=a^2\left(a-1\right)-\left(a-1\right)=\left(a-1\right)\left(a^2-1\right)=\left(a-1\right)^2\left(a+1\right)\)
f) \(x^3-2xy-x^2y+2y^2=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x-y\right)\left(x^2-2y\right)\)
a, \(=\left(a^2+b^2-2ab\right)\left(a^2+b^2+2ab\right)=\left(\left(a-b\right)\left(a+b\right)\right)^2=\left(a^2-b^2\right)^2\)
\(b,=3x\left(x-y\right)-5\left(x-y\right)=\left(x-y\right)\left(3x-5\right)\)
\(c,=-\left(x^2-3x^2+3x-1\right)=-\left(x-1\right)^3\)
\(d,=2\left(x^2+2xy+y^2-4z^2\right)=2\left(\left(x+y\right)^2-4z^2\right)=2\left(x+y-2z\right)\left(x+y+2z\right)\)
\(e,=a^2\left(a-1\right)-\left(a-1\right)=\left(a-1\right)\left(a^2-1\right)\)
\(f,=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x^2-2y\right)\left(x-y\right)\)
1. Phân tích đa thức thành nhân tử:
a. (ab-1)^2+(a+b)^2
b. x^3+2x^2+2x+1
c. x^3-sx^2+12x-27
d. x64-2x^3+2x-1
e. x^4+2x^3+2x^2+2x+1
f. x^2-2x-4y^2-4y
g. x^4+2x^3-4x-4
h. x^2(1-x^2)-4-4x^2
i. (1+2x)(1-2x)-x(x+2)(x-2)
j. x^2+y^2-x^2.y^2+xy-x-y
2.Phân tích đa thức thành nhân tử:
a. a(b^2+c^2+bc)+b(c^2+a^2+ac)+c(a^2+b^2+ab)
b.(a+b+c)(ab+bc+ca)-abc
c. a(a+2b)^3-b(2a+b)^3
Phân tích đa thức thành nhân tử
a) (1-2x)(1+2x)-x(x+2)(x-2)
b) a(a+2b)3-b(2a+b)3
c) a3(c-b2)+b3(a-c2)+c3(b-a2)+abc(abc-1)
Phân tích đa thức thành nhân tử
a) (1-2x)(1+2x)-x(x+2)(x-2)
\(=1-4x^2-x\left(x^2-4\right)\)
\(=1-4x^2-x^3+4x\)
\(=\left(1-x^3\right)+\left(4x-4x^2\right)\)
\(=\left(1-x\right)\left(1+x+x^2\right)+4x\left(1-x\right)\)
\(=\left(1-x\right)\left(1+x+x^2+4x\right)\)
\(=\left(1-x\right)\left(x^2+5x+1\right)\)
\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+12a^2b^2+8b^3a-8a^3b-12a^2b^2+6ab^3-b^4\)
\(=a^4+6a^3b+8b^3a-8a^3b-6ab^3-b^4\)
\(=\left(a^4-b^4\right)+\left(6a^3b-6ab^3\right)+\left(8b^3a-8a^3b\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3\right)+6ab\left(a^2-b^2\right)+8ab\left(b^2-a^2\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3\right)+6ab\left(a-b\right)\left(a+b\right)-8ab\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3+6a^2b+6ab^2-8a^2b-8ab^2\right)\)
\(=\left(a-b\right)\left(a^3-a^2b-ab^2+b^3\right)\)
\(=\left(a-b\right)\left[a^2\left(a-b\right)-b^2\left(a-b\right)\right]\)
\(=\left(a-b\right)^3\left(a+b\right)\)
\(a^3\left(c-b^2\right)+b^3\left(a-c^2\right)+c^3\left(b-a^2\right)+abc\left(abc-1\right)\)
\(=a^3\left(c-b^2\right)+ab^3-b^3c^2+bc^3-c^3a^2+a^2b^2c^2-abc\)
\(=a^3\left(c-b^2\right)-a^2c^2\left(c-b^2\right)-ab\left(c-b^2\right)+bc^2\left(c-b^2\right)\)
\(=\left(c-b^2\right)\left(a^3-a^2c^2-ab+bc^2\right)\)
\(=\left(c-b^2\right)\left[a^2\left(a-c^2\right)-b\left(a-c^2\right)\right]\)
\(=\left(c-b^2\right)\left(a-c^2\right)\left(a^2-b\right)\)
Phân tích đa thức thành nhân tử :
a) C = ( x^2 - 2x + 3 )( x^2 - 2x + 5 ) - 8
b) D = x^8 + x^7 + 1
ủa phần a mình phân tích rồi mà bạn hu hu