tính
a)2x^2+98-28x
b)5x^2-20y^2
c)4x^2-324
d)3a^2+6ab+3b^2
e)(a-4)^2-4y^2
f)2x^3+16
tính
a)2x^2+98-28x
b)5x^2-20y^2
c)4x^2-324
d)3a^2+6ab+3b^2
e)(a-4)^2-4y^2
f)2x^3+16
phân tích đa thức thành nhân tử
a, x^2-y^2-2x+2y
b, 2x+2y-x^2-xy
c, 3a^2-6ab+3b^2-12c^2
d,x^2-25+y^2-2xy
e, a^2+2ab+b^2-ac-bc
f,x^2-2x-4y^2-4y
g,x^2y-x^3-9y+9x
h,x^2(x-1)+16(1-x)
\(a,x^2-y^2-2x+2y=\left(x^2-y^2\right)-\left(2x-2y\right)=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)=\left(x-y\right)\left(x+y-2\right).\) \(b,2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(x+y\right)\left(2-x\right)\)
\(c,3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3.\left(\left(a-b\right)^2-\left(2c\right)^2\right)\)
\(=3\left(a-b-2c\right).\left(a-b+2c\right)\)
\(d,x^2-25+y^2-2xy=\left(x^2-2xy+y^2\right)-5^2=\left(x-y\right)^2-5^2\)
\(=\left(x-y+5\right)\left(x-y-5\right)\)
\(e,a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b\right)\left(a+b-c\right)\)
\(f,x^2-2x-4y^2-4y=\left(x^2-4y^2\right)-\left(2x+4y\right)=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\(h,x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\)
\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
Bài 3: Phân tích các đa thức sau thành nhân tử
a) x^2 - y^2 - 2x + 2y;
b) 2x +2y - x^2 - xy;
c) 3a^2 - 6ab + 3b^2 - 12c^2 ;
d) x^2 - 25 + y^2 + 2xy;
e) a^2 + 2ab + b^2 - ac - bc;
f) x^2 - 2x - 4y^2 - 4y;
h) x^2(x-1) + 16(1-x);
g) x^2y - x^3 - 9y + 9x;
\(x^2-y^2-2x+2y=\left(x+y\right)\left(x-y\right)-2\left(x-y\right)=\left(x+y-2\right)\left(x-y\right)\) \(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left(a-b\right)^2-3\left(2c\right)^2=3\left(a-b+2c\right)\left(a-b-2c\right)\) \(x^2-25+y^2+2xy=\left(x+y\right)^2-25=\left(x+y-5\right)\left(x+y+5\right)\)
\(a^2+2ab+b^2-ac-bc=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b\right)\left(a+b-c\right)\)
\(x^2-2x+1-4y^2-4y-1=\left(x-1\right)^2-\left(2y+1\right)^2=\left(x+2y\right)\left(x-2y-2\right)\)\(x^2\left(x-1\right)-16\left(x-1\right)=\left(x-1\right)\left(x^2-16\right)=\left(x-1\right)\left(x+4\right)\left(x-4\right)\) \(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(y-x\right)\left(x^2-9\right)\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
Phân tích các đa thức sau thành nhân tử:
a) 2x^2 - 2xy - 5x +5y ; b) 8x^2 + 4xy - 2ax - ay
c) x^3 - 4x^2 + 4x ; d) 2xy - x^2 - y^2 + 16
e) x^2 - y^2 - 2yz - z^2; g) 3a^2 - 6ab + 3b^2 - 12c^2
a) 2x^2 - 2xy - 5x +5y
= (2x^2 - 2xy ) - ( 5x- 5 y)
=2x(x-y) - 5(x-y)
=(x- y). (2x- 5)
b)8x2 +4xy-2ax-ay
=(8x2 +4xy) -(2ax+ay)
=4x(2x+y)-a(2x+y)
=(2x+y).(4x-a)
c)=x(x2 -4x +4)
=x(x-2)2
d)=16- (x2 -2xy +y^2)
=4^2-(x-y)^2
=(4-x+y).(4+x-y)
các câu còn lại tg tự
chúc bn hok tốt
Phân tích các đa thức sau thành nhân tử.
a/ 3a +3b – a^2 – ab
b/ x2^ + x + y^2 – y – 2xy
c/ - x^2 + 7x – 6
d/ 5x^3y – 10x^2y^2 + 5xy^3
e/ 2x2+7x – 15
g/ x^2 -2x+2y-xy
h/ x +4x 16 +4 - 16+4y^2
a) 3a +3b -a2-ab
= 3.(a+b) -a.(a+b)=(3-a).(a+b)
b) x2 +x +y2-y-2xy
=(x2 - 2xy+y2) +(x-y)
=(x-y).(x-y+1)
c) -x2 +7x -6
= -x2 + x +6x-6
= x.(1-x) -6.(1-x) = (1-x).(x-6)
d) 5x3y -10x2y2 +5xy3
= 5xy.(x2 -2xy +y2) = 5xy.(x-y)2
e) 2x2 +7x -15
= 2x2 -3x +10x -15
=x.(2x-3) + 5.(2x-3)
=(2x-3).(x+5)
g) x2 -2x +2y -xy
=x.(x-2)-y.(x-2)
=(x-y).(x-2)
h) bn go lai de ho mk dc k?
Phân tích đa thức thành nhân tử
a) 10(x-y)-8y(y-x)
b) 3a^2-6ab+3b^2-12c
c) a^2+2ab+b^2-ab-bc
d)x^2y-x^3-9y+9x
e) 2x+2y-x^2-xy
f) x^2-25+y^2+2xy
g) x^2-2x-4y^2-4y
h) x^2(x-1)+16(1-x)
GIÚP MÌNH VỚI, MÌNH CẦN GẤP LẮM!!!
a) Ta có: 10(x-y)-8y(y-x)
\(=10\left(x-y\right)+8y\left(x-y\right)\)
\(=2\left(x-y\right)\left(5+4y\right)\)
d) Ta có: \(x^2y-x^3-9y+9x\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(y-x\right)\left(x^2-9\right)\)
\(=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
e) Ta có: \(2x+2y-x^2-xy\)
\(=2\left(x+y\right)-x\left(x+y\right)\)
\(=\left(x+y\right)\left(2-x\right)\)
f) Ta có: \(x^2-25+y^2+2xy\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
g) Ta có: \(x^2-2x-4y^2-4y\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
h) Ta có: \(x^2\left(x-1\right)+16\left(1-x\right)\)
\(=x^2\left(x-1\right)-16\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-16\right)\)
\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
Phân tích các đa thức sau thành nhân tử tổng hợp :
a, x^4 - 4x^3 + 8x^2 - 16x + 16
b, 3a^2 - 6ab + 3b^2 - 12c^2
c, a^2 + 2ab + b^2 - ac - bc
d, ac - bc - a^2 + 2ab - b^2
e, ( x - y + 5 )^2 - 2( x - y + 5) + 1
f, 2x^2 + 7x + 5
Giúp mình với mình đang cần rất gấp ạ
a) \(x^4-4x^3+8x^2-16x+16\)
\(=x^4-2x^3-2x^3+4x^2+4x^2-8x-8x+16\)
\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3-2x^2+4x-8\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\)
\(=\left(x-2\right)\left(x-2\right)\left(x^2+4\right)\)
\(=\left(x-2\right)^2\left(x^2+4\right)\)
b) \(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)
c/ \(a^2+2ab+b^2-ac-bc\)
\(=\left(a+b\right)^2-c\left(a+b\right)\)
\(=\left(a+b\right)\left(a+b-c\right)\)
d/ \(ac-bc-a^2+2ab-b^2\)
\(=c\left(a-b\right)-\left(a^2-2ab+b^2\right)\)
\(=c\left(a-b\right)-\left(a-b\right)^2\)
\(=\left(a-b\right)\left(c-a+b\right)\)
e/ \(\left(x-y+5\right)^2-2\left(x-y+5\right)+1\)
\(=\left(x-y+5\right)\left(x-y+5-2\right)+1\)
\(=\left(x-y+5\right)\left(x-y+3\right)+1\)
f/ \(2x^2+7x+5\)
\(=2x^2+2x+5x+5\)
\(=2x\left(x+1\right)+5\left(x+1\right)\)
\(=\left(x+1\right)\left(2x+5\right)\)
bài 1 : điền vào chỗ chấm để đk khẳng định đúng :
a) (...+...)2=x2+...+4y2
b) (...-...)2=a2-6ab+...
c) (...+...)2=...+m+1/4
d) 25a2-...=(...+1/2b)(....-1/2b)
e)(....+...)^2 = 4x^2 +....+1
g)(2-x)(...+...+...)=8-x^3
h) 16a^2 - ... = (...+3)(...-3)
f)25 - ...+9y^2=(...+....)^2
bài 2 : rút gọn rùi tính giá trị biểu thức :
a) A = (a-3b)2-(a+3b)2-(a-1)(b-2) vs a=1/2 . b=3
b) B = (2x-5)(2x+5)-(2x+1)2 va x = - 2005
bài 3 : tìm x :
1/ (x-2)^2 - (x+3^2 - 4(x+1)=5
2/ (2x-3)(2x+3)-(x-1)^2 - 3x(x-5)= -44
3/ (5x+1)^2 - (5x+3)(5x-3)=30
4/ (x+3)^2 +(x-2)(x+2)-2(x-1)^2=7
5/ (x+3)(x^2-3x+9)-x(x-2)(x+2)=15
6 / (x+2)^3 - x(x-3)(x+3)-6x^2=29
bài 4 : tính :
a) (x+1)(x^2-x+1)
b) (x-2)(x^2+2x+4)
c)(1-x)(1+x+x^2)
d) a^3+3a^2+3a+1
e) b^3-6b^2+12b-8
ai nhanh mk tik nha , thanks , làm bài nào cx đk !! 1 bài cx k sao , nhưng pk đúng !!
a) (x+2y)2=x2+4xy+4y2
b) (a-3b)2=a2- 6ab+9b2
bài 1 : điền vào chỗ chấm để đk khẳng định đúng :
a) (.x..+2y...)2=x2+..4y.+4y2
b) (.a..-.3b..)2=a2-6ab+.9b2..
c) (.m..+.\(\frac{1}{2}\)..)2=.m2..+m+1/4
d) 25a2-..\(\frac{1}{4}b\).=(.5a..+1/2b)(..5a..-1/2b)
e)(.2x...+.1..)^2 = 4x^2 +.4x..+1
g)(2-x)(.4..+.2x..+.x2..)=8-x^3
h) 16a^2 - ..9. = (..4a.+3)(..4a.-3)
f)25 - ..30y.+9y^2=(..5.+...3y.)^2
bài 4 : tính :
a) (x+1)(x^2-x+1)= x3+ 1
b) (x-2)(x^2+2x+4)= x3- 2
c)(1-x)(1+x+x^2)= 1 - x3
d) a^3+3a^2+3a+1 = (a + 1 )3
e) b^3-6b^2+12b-8 = (b - 2 )3
Phân tích đa thức thành các nhân tử:
a)x^2-(a+b)x+ab
b)7x^3-3xyz-21x^2+9z
c)4x+4y-x^2(x+y)
d)y^2+y-x^2+x
e)4x^2-2x-y^2-y
f)9x^2-25y^2-6x+10y
Phân tích đa thức thành nhân tử
a)(5x-4)(4x-5)-(x-3)(x-2)-(5x-4)(3x-2)
b)(5x-4)(4x-5)+(5x-1)(x+4)+3(3x-2)(4-5x)
c)(5x-4)^2+(16-25x^2)+(5x-4)(3x+2)
d)x^4-x^3-x+1
e)x^6-x^4+2x^3+2x^2
a)x^2-(a+b)x+ab
= x^2 - ax - bx + ab
= (x^2 - ax) - (bx - ab)
= x(x-a) - b(x-a)
= (x-b)(x-a)
b)7x^3-3xyz-21x^2+9z
=
c)4x+4y-x^2(x+y)
= 4(x + y) - x^2(x+y)
= (4-x^2) (x+y)
= (2-x)(2+x)(x+y)
d) y^2+y-x^2+x
= (y^2 - x^2) + (x+y)
= (y-x)(y+x)+ (x+y)
= (y-x+1) (x+y)
e)4x^2-2x-y^2-y
= [(2x)^2 - y^2] - (2x +y)
= (2x-y)(2x+y) - (2x+y)
= (2x -y -1)(2x+y)
f)9x^2-25y^2-6x+10y
=