Viết tổng sau thành tích :a) (x-y)^3 -1-3(x-y)(x-y-1)
b) x^3 + 2x^2 -3x-6
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NL
Nguyễn Lê Phước Thịnh
CTVHS
12 tháng 10 2021
Bài 2:
a: \(3x^2-3xy=3x\left(x-y\right)\)
b: \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)
c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)
d: \(x^2-y^2+2y-1=\left(x-y+1\right)\left(x+y-1\right)\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
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: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)
\(=3\left(3x-2\right)\left(x-2\right)\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
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: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
2 tháng 8 2022
a: \(=25x^2+5x-50x-10\)
\(=25x^2-45x-10\)
b: \(=27x^3+9x^2+x+\dfrac{1}{27}\)
c: \(=x^2-x+\dfrac{1}{4}\)
e: \(=x^3-1\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
27 tháng 6
3: \(x^2\left(x-1\right)+2x\left(1-x\right)\)
\(=x^2\left(x-1\right)-2x\cdot\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-2x\right)=x\left(x-1\right)\left(x-2\right)\)
5: \(y^2\left(x^2+y\right)-z\cdot x^2-zy\)
\(=y^2\left(x^2+y\right)-z\left(x^2+y\right)\)
\(=\left(x^2+y\right)\left(y^2-z\right)\)
7: \(5\left(x+y\right)^2+15\left(x+y\right)\)
\(=5\left(x+y\right)\cdot\left(x+y\right)+5\left(x+y\right)\cdot3\)
=5(x+y)(x+y+3)
9: \(7x\left(y-4\right)^2-\left(4-y\right)^3\)
\(=7x\left(y-4\right)^2+\left(y-4\right)^3\)
\(=\left(y-4\right)^2\left(7x+y-4\right)\)
11: \(\left(x+1\right)\left(y-2\right)-\left(2-y\right)^2\)
\(=\left(x+1\right)\left(y-2\right)-\left(y-2\right)^2\)
=(y-2)(x+1-y+2)
=(y-2)(x+y+3)
2: \(5x\left(x-2\right)-3x^2\left(x-2\right)\)
\(=\left(x-2\right)\left(5x-3x^2\right)=x\left(5-3x\right)\left(x-2\right)\)
4: 3x(x-5y)-2y(5y-x)
=3x(x-5y)+2y(x-5y)
=(x-5y)(3x+2y)
6: b(a-c)+5c-5a
=b(a-c)-5(a-c)
=(a-c)(b-5)
8: 9x(x-y)-10(y-x)^2
=9x(x-y)-10(x-y)^2
=(x-y)(9x-10x+10y)
=(x-y)(-x+10y)
10: \(\left(a-b\right)^2-\left(a+b\right)\left(b-a\right)\)
\(=\left(a-b\right)^2+\left(a+b\right)\left(a-b\right)\)
=(a-b)(a-b+a+b)
=2a(a-b)
12: 2x(x-3)+y(x-3)+(3-x)
=(x-3)(2x+y)-(x-3)
=(x-3)(2x+y-1)
L
1 tháng 8 2021
a) \(=2\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=2\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(2-x+y\right)\)
1 tháng 8 2021
b) \(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+y^3\right)+\left(3x^2+3xy^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2+3xy-1\right)\)
\(=\left(x+y\right)\left(x^2+y^2+2xy-1\right)\)
B
9 tháng 9 2020
Bài làm :
\(\text{a)}9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)
\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)
\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)
\(=\left(-x-3y-5\right)\left(7x+9y-1\right)\)
\(\text{b)}3x^4y^2+3x^3y^2+3xy^2+3y^2\)
\(=\left(3x^4y^2+3xy^2\right)+\left(3x^3y^2+3y^2\right)\)
\(=3xy^2\left(x^3+1\right)+3y^2\left(x^3+1\right)\)
\(=\left(3xy^2+3y^2\right)\left(x^3+1\right)\)
\(=3y^2\left(x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
\(=3y^2\left(x+1\right)^2\left(x^2-x+1\right)\)
\(\text{c)}\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)
\(=\left(x+y-1\right)\left(x^2+x+y^2+y+1-xy\right)\)
\(d ) x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
25 tháng 7 2016
\(\left(3x+1\right)^2-4\left(x-2\right)^2=9x^2+6x+1-4\left(x^2-4x+4\right)=9x^2+6x+1-4x^2+16x-16=5x^2+22x-15=\)
\(\left(5x-3\right)\left(x+5\right)\)
25 tháng 7 2016
\(9\left(2x+3\right)^2-4\left(x+1\right)^2=9\left(4x^2+12x+9\right)-4\left(x^2+2x+1\right)=36x^2+108x+81-4x^2-8x-4=32x^2+100x+77\)
\(\left(8x+11\right)\left(4x+7\right)\)
NL
Nguyễn Lê Phước Thịnh
CTVHS
8 tháng 10
1: \(3x\left(x-1\right)+7x^2\left(x-1\right)\)
\(=\left(x-1\right)\left(7x^2+3x\right)\)
=x(7x+3)(x-1)
2: \(9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15\right)^2-\left(x-7\right)^2\)
=(3x+15+x-7)(3x+15-x+7)
=(4x+8)(2x+22)
\(=4\left(x+2\right)\cdot2\cdot\left(x+11\right)=8\left(x+2\right)\left(x+11\right)\)
3: \(x^2-2xy+y^2-xz+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
=(x-y)(x-y-z)
4: \(\left(x^2+2x\right)^2-2x^2-4x-3\)
\(=\left(x^2+2x\right)^2-2\cdot\left(x^2+2x\right)-3\)
\(=\left(x^2+2x-3\right)\left(x^2+2x+1\right)=\left(x+3\right)\left(x-1\right)\left(x+1\right)^2\)
5: \(9x^2y^2+15x^2y-21xy^2\)
\(=3xy\cdot3xy+3xy\cdot5x-3xy\cdot7y\)
=3xy(3xy+5x-7y)
6: \(x^3-2x^2y+xy^2-9xy^4\)
\(=x\left(x^2-2xy+y^2-9y^4\right)\)
\(=x\left\lbrack\left(x-y\right)^2-\left(3y^2\right)^2\right\rbrack=x\left(x-y-3y^2\right)\left(x-y+3y^2\right)\)
7: \(x^2+x-12\)
\(=x^2+4x-3x-12\)
=x(x+4)-3(x+4)
=(x+4)(x-3)
8: (x+1)(x+3)(x+5)(x+7)+15
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
\(=\left(x^2+8x+7\right)^2+8\left(x^2+8x+7\right)+15\)
\(=\left(x^2+8x+7+3\right)\left(x^2+8x+7+5\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)