* Phân tích đa thức thành nhân tử:
1/ 25x2 - 10xy + y2
2/ 8x3 + 36x2y + 54xy2 + 27y3
3/ (a2 + b2 - 5)2 - 4 (ab + 2)2
4/ (a + b + c)3 - a3 - b3 - c3
5/ 2x3 + 3x2 + 2x + 3
6/ x3z + x2yz - x2z2 - xyz2
7/ x3 + y (1 - 3x2) + x (3y2 - 1) - y3
8/ x3 + 3x2y + 3xy2 + y + y3
9/ x2 - 6x + 8
10/ x2 - 8x + 12
11/ a2 (b - c) + b2 (c - a) + c2 (a - b)
12/ x3 - 7x - 6
13/ x4 + 4
14/ a4 + 64
15/ x5 + x + 1
16/ x5 + x - 1
17/ (x2 + x)2 - 2 (x2 + x) - 15
18/ (x + 2) (x + 3) (x + 5) - 24
19/ (x2 + 8x + 7) (x2 + 8x + 15) + 15
20/ (x2 + 3x + 1) (x2 + 3x + 2) - 6
21/ x2 + 4xy + 3y2
22/ 2x2 - 5xy + 2y2
23/ x2 (y - z) + y2 (z - x) + z2 (x - y)
24/ 2x2 - 7xy + 3y2 + 5xz - 5yz + 2z2
25/ x2 - 7x + 10
26/ 4x2 - 3x - 1
27/ x2 - x - 12
28/ bc (b + c) + ac (c - a) - ab (a + b)
29/ x2y + xy2 + x2z + xz2 + y2z + yz2 + 2xyz
30/ (a - b)3 + (b - c)3 + (c - a)3
31/ ab (a - b) + bc (b - c) + ca (c - a)
32/ bc (b + c) + ca (c + a) + ba (a + b) + 2abc
Giúp mình với, giải chi tiết nha, nhiều bài mà mình đang cần gấp lắm!
1, \(25x^2-10xy+y^2=\left(5x-y\right)^2\)
2, \(8x^3+36x^2y+54xy^2+27y^3=\left(2x+3y\right)^3\)
4, \(\left(a+b+c\right)^3-a^3-b^3-c^3\)
\(=a^3+b^3+c^3+3\left(a+b\right)\left(b+c\right)\left(a+c\right)-a^3-b^3-c^3\)
\(=3\left(a+b\right)\left(b+c\right)\left(a+c\right)\)
5, \(2x^3+3x^2+2x+3\)
\(=x^2\left(2x+3\right)+2x+3\)
\(=\left(x^2+1\right)\left(2x+3\right)\)
6, \(x^3z+x^2yz-x^2z^2-xyz^2\)
\(=x^3z-x^2z^2+x^2yz-xy^2\)
\(=xz\left(x^2-xz\right)+xz\left(xy-yz\right)\)
\(=xz\left[x\left(x-z\right)+y\left(x-z\right)\right]\)
\(=xz\left(x+y\right)\left(x-z\right)\)
8, \(x^3+3x^2y+3xy^2+y+y^3\)\(=\left(x+y\right)^3+y\)
9, \(x^2-6x+8\)
\(=x^2-4x-2x+8\)
\(=x\left(x-4\right)-2\left(x-4\right)\)
\(=\left(x-2\right)\left(x-4\right)\)
10, \(x^2-8x+12\)
\(=x^2-6x-2x+12\)
\(=x\left(x-6\right)-2\left(x-6\right)\)
\(=\left(x-2\right)\left(x-6\right)\)
Chỗ còn lại mai làm nốt nha.
Gặp chút sự cố đăng nhập nên hơi muộn, xin lỗi nha
11, \(a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)\)
\(=a^2b-a^2c+b^2c-b^2a+c^2a-c^2b\)
\(=a^2b-ab^2+abc-a^2c+b^2c-abc+ac^2-c^2b\)
\(=ab\left(a-b\right)-ac\left(a-b\right)-bc\left(a-b\right)+c^2\left(a-b\right)\)
\(=\left(a-b\right)\left(ab-ac-bc+c^2\right)\)
\(=\left(a-b\right)\left[b\left(a-c\right)-c\left(a-c\right)\right]\)
\(=\left(a-b\right)\left(a-c\right)\left(b-c\right)\)
12, \(x^3-7x-6\)
\(=x^3-3x^2+3x^2-9x+2x-6\)
\(=x^2\left(x-3\right)+3x\left(x-3\right)+2\left(x-3\right)\)
\(=\left(x-3\right)\left(x^2+3x+2\right)\)
\(=\left(x-3\right)\left(x^2+x+2x+2\right)\)
\(=\left(x-3\right)\left[x\left(x+1\right)+2\left(x+1\right)\right]\)
\(=\left(x-3\right)\left(x+2\right)\left(x+1\right)\)
13, \(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
14, \(a^4+64\)
\(=a^4+16a^2+64-16a^2\)
\(=\left(a^2+8\right)^2-16a^2\)
\(=\left(a^2-4a+8\right)\left(a^2+4a+8\right)\)
15, \(x^5+x+1\)
\(=x^5-x^2+x^2+x+1\)
\(=x^2\left(x^3-1\right)+x^2+x+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)+x^2+x+1\)
\(=\left(x^2+x+1\right)\left[x^2\left(x-1\right)+1\right]\)
16, \(x^5+x-1\)
\(=x^5-x^4+x^3+x^4-x^3+x^2-x^2+x-1\)
\(=x^3\left(x^2-x+1\right)-x^2\left(x^2-x+1\right)-\left(x^2-x+1\right)\)
\(=\left(x^2-x+1\right)\left(x^3-x^2-1\right)\)
17, \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
\(=\left(x^2+x\right)\left(x^2+x-2\right)-15\)
19, \(\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\) (*)
Đặt \(x^2+8x+7=a\) ta có:
(*) \(\Leftrightarrow a\left(a+8\right)+15\)
\(\Leftrightarrow a^2+8a+15\)
\(\Leftrightarrow a^2+3a+5a+15\)
\(\Leftrightarrow a\left(a+3\right)+5\left(a+3\right)\)
\(\Leftrightarrow\left(a+3\right)\left(a+5\right)\)
Trả lại biến cũ ta có: (*) \(\Leftrightarrow\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
20, \(\left(x^2+3x+1\right)\left(x^2+3x+2\right)-6\) (*)
Đặt \(x^2+3x+1=a\) ta có:
(*) \(\Leftrightarrow a\left(a+1\right)-6\)
\(\Leftrightarrow a^2+a-6\)
\(\Leftrightarrow a^2+3a-2a-6\)
\(\Leftrightarrow a\left(a+3\right)-2\left(a+3\right)\)
\(\Leftrightarrow\left(a-2\right)\left(a+3\right)\)
Trả lại biến cũ ta có: (*) \(\Leftrightarrow\left(x^2+3x-1\right)\left(x^2+3x+5\right)\)
21, \(x^2+4xy+3y^2\)
\(=x^2+4xy+4y^2-y^2\)
\(=\left(x+2y\right)^2-y^2\)
\(=\left(x+2y-y\right)\left(x+2y+y\right)\)
\(=\left(x+y\right)\left(x+3y\right)\)
22, \(2x^2-5xy+2y^2\)
\(=2x^2-xy-4xy+2y^2\)
\(=x\left(2x-y\right)-2y\left(2x-y\right)\)
\(=\left(x-2y\right)\left(2x-y\right)\)
23, \(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\) (giống câu 11, chỉ cần thêm bớt xyz)
24, \(2x^2-7xy+3y^2+5xz-5yz+2z^2\)
\(=2x^2-xy+xz-6xy+3y^2-2yz+4xz-3yz+2z^2\)
\(=2x\left(x-3y+2z\right)-y\left(x-3y+2z\right)+z\left(x-3y+2z\right)\)
\(=\left(2x-y+z\right)\left(x-3y+2z\right)\)
25, \(x^2-7x+10\)
\(=x^2-2x-5x+10\)
\(=x\left(x-2\right)-5\left(x-2\right)\)
\(=\left(x-5\right)\left(x-2\right)\)
26, \(4x^2-3x-1\)
\(=4x^2-4x+x-1\)
\(=4x\left(x-1\right)+x-1\)
\(=\left(4x+1\right)\left(x-1\right)\)
27, \(x^2-x-12\)
\(=x^2-4x+3x-12\)
\(=x\left(x-4\right)+3\left(x-4\right)\)
\(=\left(x-4\right)\left(x+3\right)\)
28, \(bc\left(b+c\right)+ac\left(c-a\right)-ab\left(a+b\right)\)(giải tương tự câu 11, thêm bớt abc)
29, \(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz\)
\(=\left(x^2y+xy^2+xyz\right)+\left(x^2z+xz^2+xyz\right)+\left(y^2z+yz^2\right)\)
\(=xy\left(x+y+z\right)+xz\left(x+y+z\right)+yz\left(y+z\right)\)
\(=\left(x+y+z\right)\left(xy+xz\right)+yz\left(y+z\right)\)
\(=x\left(y+z\right)\left(x+y+z\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left[x\left(x+y+z\right)+yz\right]\)
\(=\left(y+z\right)\left(x^2+xy+xz+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+y\right)+z\left(x+y\right)\right]\)
\(=\left(x+y\right)\left(x+z\right)\left(y+z\right)\)
Còn 3 câu cuối tính sau, mệt