Phan tich da thuc sau thanh nhan tu
a, x^2+2*x*y+y^2-x-y-12
b, 4*x^4-32*x^2+1
c, 3*(x^4+x^2+1)-(x^2+x+1)^2
d,6+x^4+y^4
e, a^6+a^4+a*b^2+b^2-b^6
giai ho mk nha , mk dag can gap=> mon nhiu lem a
BAI 1.phan tich cac da thuc sau thanh nhan tu:
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
BAI 2.tinh nhanh
a,37,5.8,5-7,5.3,4-6,6.7,5+1,5.37,5
b,35^2+40^2-25^2+80.35
BAI 3. Tim x biet:
a,x^3-1/9x=0
b,2x-2y-x^2+2xy-y^2=0
c,x(x-3)+x-3=0
d,x^2(x-3)+27-9x=0
BAI 4.Phan tich cac da thuc sau thanh nhan tu
a,x^2-4x+3
goi y :tach-4x=-x3xhoac tach3=-1+4
b,x^2+x-6
c,x^2-5x+6
d,x^4+4 (goi y:them va bot 4x^2)
BAI 5.Chung minh rang;
(3n+4)^2-16 chia het cho 3 voi moi so nguyen n.
BAI 6.Tinh gia tri cua bieu thuc sau:
M=a^3-a^2b-ab^2+b^3 voi a=5,75:b=4,25
BAI 7.Tim x biet:
a,x^2+x=6
b,6x^3+x^2=2x
Bài 1 câu g bạn kia làm sai mình sửa lại nhá
\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2\right)-12c^2\)
\(=3\left(a-b\right)^2-12c^2\)
\(=3\left[\left(a-b\right)^2-4c^2\right]\)
\(=3\left(a-b-2c\right)\left(a-b+2c\right)\)
Để mình làm tiếp cho :))
Bài 2 :
Câu a : \(37,5.8,5-7,5.3,4-6,6.7,5+1,5.37,5\)
\(=\left(37,5.8,5+1,5.37,5\right)-\left(7,5.3,4+6,6.7,5\right)\)
\(=37,5\left(8,5+1,5\right)-7,5\left(3,4+6,6\right)\)
\(=37,5.10-7,5.10\)
\(=10.30=300\)
Câu b : \(35^2+40^2-25^2+80.35\)
\(=\left(35^2+80.35+40^2\right)-25^2\)
\(=\left(30+45\right)^2-25^2\)
\(=75^2-25^2\)
\(=\left(75+25\right)\left(75-25\right)\)
\(=100.50=5000\)
Bài 3 :
Câu a : \(x^3-\dfrac{1}{9}x=0\)
\(\Leftrightarrow x\left(x^2-\dfrac{1}{9}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2-\dfrac{1}{9}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=\pm\dfrac{1}{3}\end{matrix}\right.\)
Câu b : \(2x-2y-x^2+2xy-y^2=0\)
\(\Leftrightarrow2\left(x-y\right)-\left(x-y\right)^2=0\)
\(\Leftrightarrow\left(x-y\right)\left(2-x+y\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-y=0\\2-x+y=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=y\\x+y=2\Rightarrow x=2-y\end{matrix}\right.\)
Câu c :
\(x\left(x-3\right)+x-3=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
\(x^2\left(x-3\right)+27-9x=0\)
\(\Leftrightarrow x^2\left(x-3\right)-9\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x^2-9=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=3\\x=\pm3\end{matrix}\right.\)
Bài 4 :
Câu a :
\(x^2-4x+3\)
\(=x^2-x-3x+3\)
\(=\left(x^2-x\right)-\left(3x-3\right)\)
\(=x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x-1\right)\left(x-3\right)\)
Câu b :
\(x^2+x-6\)
\(=x^2-2x+3x-6\)
\(=x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(x-2\right)\left(x+3\right)\)
Câu c :
\(x^2-5x+6\)
\(=x^2-2x-3x+6\)
\(=\left(x^2-2x\right)-\left(3x-6\right)\)
\(=x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x-2\right)\left(x-3\right)\)
Câu d :
\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
Bài 1:
a) \(2x^2-2xy-5x+5y\)
\(=\left(2x^2-2xy\right)-\left(5x-5y\right)\)
\(=2x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(2x-5\right)\)
b) \(8x^2+4xy-2ax-ay\)
\(=\left(8x^2+4xy\right)-\left(2ax+ay\right)\)
\(=4x\left(2x+y\right)-a\left(2x+y\right)\)
\(=\left(2x+y\right)\left(4x-a\right)\)
c) \(x^3-4x^2+4x\)
\(=x\left(x^2-4x+4\right)\)
\(=x\left(x-2\right)^2\)
d) \(2xy-x^2-y^2+16\)
\(=-\left[\left(x^2-2xy+y^2\right)-16\right]\)
\(=-\left[\left(x-y\right)^2-4^2\right]\)
\(=-\left[\left(x-y-4\right)\left(x-y+4\right)\right]\)
e) \(x^2-y^2-2yz-z^2\)
\(=-\left[\left(z^2+2yz+y^2\right)-x^2\right]\)
\(=-\left[\left(z+y\right)^2-x^2\right]\)
\(=-\left[\left(z+y+x\right)\left(z+y-x\right)\right]\)
g) \(3a^2-6ab+3b^2-12c^2\)
\(=\left(3a^2-6ab+3b^2\right)-12c^2\)
\(=\left(\sqrt{3a}+\sqrt{3b}\right)^2-12c^2\)
\(=\left(\sqrt{3a}+\sqrt{3b}+\sqrt{12c}\right)\left(\sqrt{3a}+\sqrt{3b}-\sqrt{12c}\right)\)
phan tich da thuc thanh nhan tu:
a,x^4-2x^3-12x^2+12x+36
b,x^4+x^3+6x^2+5x+5
c,x^8y^8+x^4y^4+1
d,x^5-x^4+x^3-X^2+x-1
e,x^5+x^4-X63+x62-x+2
g,x(Y^2-z^2)+y(z^2-x^2)+z(x^2-y^2)
phan tich da thuc thanh nhan tu :
a) x3-5x2+5x-5
b) x3+42+x-6
c) x3+ y3+6x2+12x +8
a: Sửa đề: x^3-x^2+5x-5
=x^2(x-1)+5(x-1)
=(x-1)(x^2+5)
b: x^3+4x^2+x-6
=x^3-x^2+5x^2-5x+6x-6
=(x-1)(x^2+5x+6)
=(x-1)(x+2)(x+3)
c: \(=\left(x+2\right)^3+y^3\)
\(=\left(x+2+y\right)\left(x^2+4x+4-xy-2y+y^2\right)\)
phan tich da thuc thanh nhan tu
a, x^2+x-6
b,x^4+4
a)\(x^2+x-6\)
\(=x^2-2x+3x-6\)
\(=\left(x^2-2x\right)+\left(3x-6\right)\)
\(=x\left(x-2\right)+3\left(x-2\right)\)
\(=\left(x-2\right)\left(x+3\right)\)
a) x2 + x - 6
= x2 - 2x + 3x - 6
= (x2 - 2x) + (3x - 6)
= x(x - 2) + 3(x - 2)
= (x + 3)(x - 2)
b) x4 + 4
= x4 + 4x2 + 4 - 4x2
= (x4 + 4x2 + 4) - 4x2
= (x + 2)2 - 4x2
= (x + 2 - 2x)(x + 2 +2x)
1. phan tich da thuc thanh nhan tu
a. x^2+3x-5 b. 4x^2-16x+7 c. 5x^2-6x-7 d.x^4+2x^3-4x-4
2. tim x,y bt: x^2+y^2+z^2=xy+yz+zx va x^2012+y^2012+z^2012= 3^2013
3. tim x: a. x^2-4x=21 b. x^2-4x+4=0 c.x^2-6x=2x=11 d. 4^x-12.2^x+32=0
Cach phan tich da thuc thanh nhan tu
a)X^3+2X^2+2X+1
b)X^3-4X^2+12X-27
c)a^6-a^4+2a^3+2a^2
d)x^4+2x^3+2x^2+2x+1
e)x^5+x^4+x^3+x^2+x+1
a)
=x3+x2+x2+x+x+1
=x2(x+1)+x(x+1)+(x+1)
=(x+1)(x2+x+1)
b)
=x3-3x2-x2+3x+9x-27
=x2(x-3)-x(x-3)+9(x-3)
=(x-3)(x2-x+9)
a)
=x3+x2+x2+x+x+1
=x2(x+1)+x(x+1)+(x+1)
=(x+1)(x2+x+1)
b)
=x3-3x2-x2+3x+9x-27
=x2(x-3)-x(x-3)+9(x-3)
=(x-3)(x2-x+9)
d)x^4+2x^3+2x^2+2x+1(no)
e)x^5+x^4+x^3+x^2+x+1 ( no)
1) Phan tich da thuc sau thanh nhan tu: x2-x-2008.2009
2) Chung minh rang voi moi x,y,z ta luon co: x2+4y2+z2>=2x+12y+4z
3) Cho a-b=4. Tinh gia tri cua bieu thuc: a3-12ab-b3
cac ban lam duoc cau nao thi giup mik nha. mik dang can gap lam
phan tich da thuc thanh nhan tu
a)x^4+x^2y^2+y^4
b)x^3+3x-4
c)x^2+9x+8
d)x^2+x-42
e)y^2-13y+12
f)x^2-x-30
g)2x^2+xy-y^2
h)y^2-y-12
i)x^2+x-2
j)x^3+3x^2-2
k)x^3-6x^2+16
l)x^3+3x+4
m)x^4+6x^3-12x^2-8x
minh can gap lam, chiu nay la minh hoc roi
\(\text{a) }x^4+x^2y^2+y^4=x^4+2x^2y^2-x^2y^2+y^4=\left(x^4+2x^2y^2+y^4\right)-\left(x^2y^2\right)=\left(x^2+y^2\right)^2-\left(xy\right)^2\)
\(=\left(x^2+y^2+xy\right)\left(x^2+y^2-xy\right)\)
\(\text{b) }x^3+3x-4=x^3+3x-1-3=\left(x^3-1\right)+\left(3x-3\right)=\left(x-1\right)\left(x^2+x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1+3\right)=\left(x-1\right)\left(x^2+x+4\right)\)
\(\text{c) }x^2+9x+8=x^2+8x+x+8=\left(x^2+8x\right)+\left(x+8\right)=x\left(x+8\right)+\left(x+8\right)\)
\(=\left(x+8\right)\left(x+1\right)\)
\(\text{d) }x^2+x-42=x^2+7x-6x-42=\left(x^2+7x\right)-\left(6x+42\right)=x\left(x+7\right)-6\left(x+7\right)\)
\(=\left(x+7\right)\left(x-6\right)\)
\(\text{e) }y^2-13y+12=y^2-y-12y+12=\left(y^2-y\right)-\left(12y-12\right)=y\left(y-1\right)-12\left(y-1\right)\)
\(=\left(y-1\right)\left(y-12\right)\)
Mấy câu sau mk sẽ giải tiếp, bạn ráng chờ nha
\(\text{f) }x^2-x-30=x^2+5x-6x-30=\left(x^2+5x\right)-\left(6x+30\right)=x\left(x+5\right)-6\left(x+5\right)\)
\(=\left(x+5\right)\left(x-6\right)\)
\(\text{g) }2x^2+xy-y^2=x^2+x^2+xy-y^2=\left(x^2-y^2\right)+\left(x^2+xy\right)=\left(x-y\right)\left(x+y\right)+x\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y+x\right)=\left(x+y\right)\left(2x-y\right)\)
\(\text{h) }y^2-y-12=y^2+3y-4y-12=\left(y^2+3y\right)-\left(4y+12\right)=y\left(y+3\right)-4\left(y+3\right)\)
\(=\left(y+3\right)\left(y-4\right)\)
phan tich da thuc thanh nhan tu B=\(\left(x^2-y^2+1\right)^3-x^6-y^6-1\)