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LH
6
25 tháng 11 2021
\(a,x\left(a-b\right)+2a-2b=x\left(a-b\right)+2\left(a-b\right)=\left(a-b\right)\left(x+2\right)\\ b,Sửa:ax+ay+5x+5y=a\left(x+y\right)+5\left(x+y\right)=\left(a+5\right)\left(x+y\right)\)
25 tháng 11 2021
\(a,=\left(x+2\right)\left(a-b\right)\\ b,Sửa:ax+ay+5x+5y\\ =a\left(x+y\right)+5\left(x+y\right)\\ =\left(a+5\right)\left(x+y\right)\)
T
1
11 tháng 8 2021
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: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)
\(=3\left(3x-2\right)\left(x-2\right)\)
11 tháng 8 2021
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: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)
HT
3
14 tháng 12 2022
a: =3x(y-2)-5(y-2)
=(y-2)(3x-5)
b: =(2x-5y)(2x+5y)
c: =x(x^3-8)
=x(x-2)(x^2+2x+4)
NH
14 tháng 12 2022
a)
\(3x\left(y-2\right)+5\left(2-y\right)\\=3x\left(y-2\right)-5\left(y-2\right)\\ =\left(y-2\right)\left(3x-5\right) \)
b)
\(4x^2-25y^2\\ =\left(2x-5y\right)\left(2x+5y\right)\)
c)
\(x^4-8x\\ =x\left(x^3-8\right)\\ =x\left(x-2\right)\left(x^2+2x+4\right)\)
6 tháng 12 2021
\(a,=4x^3\left(x+1\right)-x\left(x+1\right)=x\left(4x^2-1\right)\left(x+1\right)\\ =x\left(2x-1\right)\left(2x+1\right)\left(x+1\right)\\ b,=\left(a-1\right)^2-\left(b-c\right)^2\\ =\left(a-1-b+c\right)\left(a-1+b-c\right)\\ c,=\left(x^2-9x+14\right)\left(x^2-9x+20\right)-72\\ =\left(x^2-9x+17\right)^2-9-72\\ =\left(x^2-9x+17\right)^2-81=\left(x^2-9x+8\right)\left(x^2-9x+26\right)\\ =\left(x-1\right)\left(x-8\right)\left(x^2-9x+26\right)\)
23 tháng 10 2021
a,\(x^5+x-1=x^5+x^4-x^2-x^4-x^3+x+x^3+x^2-1=\left(x^5+x^4-x^2\right)-\left(x^4+x^3-x\right)+\left(x^3+x^2-1\right)=x^2\left(x^3+x^2-1\right)+x\left(x^3+x^2-1\right)+\left(x^3+x^2-1\right)=\left(x^2+x+1\right)\left(x^3+x^2-1\right)\)b,\(y\left(y-2\right)-5=y^2-2y-5=\left(y^2-2y+1\right)-6=\left(y-1\right)^2-\sqrt{6^2}=\left(y-1-\sqrt{6}\right)\left(y-1+\sqrt{6}\right)\)
MN
1
NV
Nguyễn Việt Lâm
Giáo viên
3 tháng 1
a.
\(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b.
\(x^3-9x^2+6x+16=\left(x^3-7x^2-8x\right)-\left(2x^2-14x-16\right)\)
\(=x\left(x^2-7x-8\right)-2\left(x^2-7x-8\right)\)
\(=\left(x-2\right)\left(x^2-7x-8\right)=\left(x-2\right)\left(x^2+x-8x-8\right)\)
\(=\left(x-2\right)\left[x\left(x+1\right)-8\left(x+1\right)\right]=\left(x-2\right)\left(x+1\right)\left(x-8\right)\)
c.
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+10+2\right)-24\)
\(=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x+10\right)^2-4\left(x^2+7x+10\right)+6\left(x^2+7x+10\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+10-4\right)+6\left(x^2+7x+10-4\right)\)
\(=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
NQ
1
22 tháng 12 2021
a) \(=x\left(x-5\right)+\left(x-5\right)^2=\left(x-5\right)\left(x+x-5\right)=\left(x-5\right)\left(2x-5\right)\)
b) \(=x^2-2.x.10+10^2=\left(x-10\right)^2\)
c) \(=x\left(x+3\right)+2\left(x+3\right)=\left(x+3\right)\left(x+2\right)\)
a5+b5−(a+b) 5
=a5+b5−a5−5a4b−10a3b2−10a2b3−5ab4−b5=a5+b5−a5−5a4b−10a3b2−10a2b3−5ab4−b5
=−5ab(a3+2a2b+2ab2+b3)=−5ab(a3+2a2b+2ab2+b3)
=−5ab(a+b)(a2+ab+b2)