Phân tích thành nhân tử ( phối hợp các phương pháp )
x2+(a+b)xy-aby2
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TN
2
PT
2
DA
25 tháng 8 2021
a) 16 + 2x3y3
= 2( 8 + x3y3)
= 2[ 23 + (xy)3]
= 2 (2+xy)(4 - 2xy + x2y2)
b) 100a2 - (a2 + 25)2
= (10a)2 - (a2 +25)2
= (10a - a2 - 25)(10a + a2 +25)
= -(a2 - 2a.5 + 52)(a2 + 2a.5 + 52)
=-(a-5)2 (a+5)2
25 tháng 8 2021
a) \(16+2x^3y^3\)
\(=2\left(8+x^3y^3\right)\)
\(=2\left(xy+2\right)\left(x^2y^2-2xy+4\right)\)
b) \(100a^2-\left(a^2+25\right)^2\)
\(=\left(10a-a^2-25\right)\left(10a+a^2+25\right)\)
\(=-\left(a-5\right)^2\left(a+5\right)^2\)
LV
1
KV
23 tháng 8 2023
2x - 2y - x² + 2xy - y²
= (2x - 2y) - (x² - 2xy + y²)
= 2(x - y) - (x - y)²
= (x - y)(2 - x + y)
27 tháng 8 2021
a: \(3x^3-75x\)
\(=3x\left(x^2-25\right)\)
\(=3x\left(x-5\right)\left(x+5\right)\)
b: \(x^4y^2-12x^3y^2+48x^2y^2-64xy^2\)
\(=xy^2\left(x^3-12x^2+48x-64\right)\)
\(=xy^2\cdot\left(x-4\right)^3\)
27 tháng 8 2021
a) \(x^4-4x^2-4x-1=\left(x^4-1\right)-4x\left(x+1\right)=\left(x^2+1\right)\left(x-1\right)\left(x+1\right)-4x\left(x+1\right)=\left(x+1\right)\left[\left(x^2+1\right)\left(x-1\right)-4x\right]=\left(x+1\right)\left(x^3-x^2+x-1-4x\right)=\left(x+1\right)\left(x^3-x^2-3x-1\right)\)
b) \(10x^4y^2-10x^3y^2-10x^2y^2+10xy^2=10xy^2\left(x^3-x^2-x+1\right)=10xy^2\left(x-1\right)^2\left(x+1\right)\)
27 tháng 8 2021
a: \(x^4-4x^2-4x-1\)
\(=\left(x^4-1\right)-4x\left(x+1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)-4x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+x-x^2-1-4x\right)\)
\(=\left(x+1\right)\left(x^3-x^2-3x-1\right)\)
b: \(10x^4y^2-10x^3y^2-10x^2y^2+10xy^2\)
\(=10xy^2\left(x^3-x^2-x+1\right)\)
\(=10xy^2\cdot\left[\left(x+1\right)\left(x^2-x+1\right)-x\left(x+1\right)\right]\)
\(=10xy^2\cdot\left(x+1\right)\left(x-1\right)^2\)
22 tháng 8 2021
a) \(5x^2y-20xy+20y=5y\left(x^2-4x+4\right)=5y\left(x-2\right)^2\)
b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)
c) \(3x^2y-12y=3y\left(x^2-4\right)=3y\left(x-2\right)\left(x+2\right)\)
d) \(7x^3-28x^2+28x=7x\left(x^2-4x+4\right)=7x\left(x-2\right)^2\)
22 tháng 8 2021
a: \(5x^2y-20xy+20y\)
\(=4y\left(x^2-4x+4\right)\)
\(=4x\left(x-2\right)^2\)
b: \(3x^3+6x^2+3x\)
\(=3x\left(x^2+2x+1\right)\)
\(=3x\left(x+1\right)^2\)
c: \(3x^2y-12y\)
\(=3y\left(x^2-4\right)\)
\(=3y\left(x-2\right)\left(x+2\right)\)
d: \(7x^3-28x^2+28x\)
\(=7x\left(x^2-4x+4\right)\)
\(=7x\left(x-2\right)^2\)
HD
1
15 tháng 12 2023
a: \(x^2-4xy+4y^2-2x+4y-35\)
\(=\left(x^2-4xy+4y^2\right)-\left(2x-4y\right)-35\)
\(=\left(x-2y\right)^2-2\left(x-2y\right)-35\)
\(=\left(x-2y\right)^2-7\left(x-2y\right)+5\left(x-2y\right)-35\)
\(=\left(x-2y\right)\left(x-2y-7\right)+5\left(x-2y-7\right)\)
\(=\left(x-2y-7\right)\left(x-2y+5\right)\)
c: \(\left(xy+ab\right)^2+\left(ay-bx\right)^2\)
\(=x^2y^2+a^2b^2+2xyab+a^2y^2-2aybx+b^2x^2\)
\(=x^2y^2+a^2y^2+a^2b^2+b^2x^2\)
\(=y^2\left(x^2+a^2\right)+b^2\left(a^2+x^2\right)\)
\(=\left(x^2+a^2\right)\left(y^2+b^2\right)\)
N
2
KN
1 tháng 8 2019
\(\left(a+4\right)^2-16a^2\)
\(=\left(a+4\right)^2-\left(4a\right)^2\)
\(=\left(a+4+4a\right)\left(a+4-4a\right)\)
\(=\left(5a+4\right)\left(4-3a\right)\)
KN
1 tháng 8 2019
\(x^3=4x\)
\(\Leftrightarrow x^3-4x=0\)
\(\Leftrightarrow x\left(x^2-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^2-4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm\sqrt{4}=\pm2\end{cases}}\)
27 tháng 8 2021
c) \(5x^2+3y+15x+xy=5x\left(x+3\right)+y\left(x+3\right)=\left(x+3\right)\left(5x+y\right)\)
d) \(x^2+6x+9-y^2=\left(x+3\right)^2-y^2=\left(x+3-y\right)\left(x+3+y\right)\)
e) \(x^2-y^2+2x+1=\left(x^2+2x+1\right)-y^2=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)
f) \(x^2-2xy-9+y^2=\left(x^2-2xy+y^2\right)-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
27 tháng 8 2021
c: \(5x^2+15x+3y+xy\)
\(=5x\left(x+3\right)+y\left(x+3\right)\)
\(=\left(x+3\right)\left(5x+y\right)\)
d: \(x^2+6x+9-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
e: \(x^2+2x+1-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1-y\right)\left(x+1+y\right)\)
f: \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-9\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
28 tháng 10 2021
Bài 1:
\(1,Sửa:x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\\ 2,=6\left(x^2+2xy+y^2\right)=6\left(x+y\right)^2\\ 3,=2y\left(y^2+4y+4\right)=2y\left(y+2\right)^2\\ 4,=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)
Bài 2:
\(1,=x\left(x^2-64\right)=x\left(x-8\right)\left(x+8\right)\\ 2,=2y\left(4x^2-9\right)=2y\left(2x-3\right)\left(2x+3\right)\\ 3,=3\left(x^3-1\right)=3\left(x-1\right)\left(x^2+x+1\right)\)
Bài 3:
\(a,=5\left(x^2+2x+1-y^2\right)=5\left[\left(x+1\right)^2-y^2\right]=5\left(x-y+1\right)\left(x+y+1\right)\\ b,=3x\left(x^2-2x+1-4y^2\right)=3x\left[\left(x-1\right)^2-4y^2\right]\\ =3x\left(x-2y-1\right)\left(x+2y-1\right)\\ c,=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\\ =\left(a+b\right)\left(a^2b-ab^2+a+b\right)\\ d,=2x\left(x^2-y^2-4x+4\right)=2x\left[\left(x-2\right)^2-y^2\right]\\ =2x\left(x-y-2\right)\left(x+y-2\right)\)
đây đâu phải đề tiếng anh bạn!!!