Phân tích đa thức thành nhân tử : (xy + 1)^2 – (x + y)^2
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KN
1
KV
26 tháng 11 2023
x²y + xy² - x - y
= (x²y + xy²) - (x + y)
= xy(x + y) - (x + y)
= (x + y)(xy - 1)
DN
2
2 tháng 9 2021
\(x^2-xy\left(a+b\right)+aby^2=x^2-xya-xyb+aby^2=x\left(x-ya\right)-yb\left(x-ya\right)=\left(x-ya\right)\left(x-yb\right)\)
2 tháng 9 2021
\(x^2-xy\left(a+b\right)+aby^2\)
\(=x^2-axy-bxy+aby^2\)
\(=x\left(x-ay\right)-by\left(x-ay\right)\)
\(=\left(x-ay\right)\left(x-by\right)\)
8 tháng 12 2023
2: \(8xy-24xy+16x\)
\(=8x\cdot y-8x\cdot3y+8x\cdot2\)
\(=8x\left(y-3y+2\right)=8x\left(-2y+2\right)\)
\(=-16y\left(y-1\right)\)
3: \(xy-x=x\cdot y-x\cdot1=x\left(y-1\right)\)
11: \(2mx-4m2xy+6mx\)
\(=2mx-2my\cdot4y+2mx\cdot3\)
\(=2mx\left(1-4y+3\right)\)
\(=2mx\left(4-4y\right)=8mx\left(1-y\right)\)
12: \(7x^2y^5-14x^3y^4-21y^3\)
\(=7y^3\cdot x^2y^2-7y^3\cdot2x^3y-7y^3\cdot3\)
\(=7y^3\left(x^2y^2-2x^3y-3\right)\)
13: \(2\left(x-y\right)-a\left(x-y\right)\)
\(=2\cdot\left(x-y\right)-a\cdot\left(x-y\right)\)
\(=\left(x-y\right)\left(2-a\right)\)
DN
2
4 tháng 9 2021
\(\left(x+y\right)^2+3\left(x+y\right)-10=\left[\left(x+y\right)^2+2\left(x+y\right).\dfrac{3}{2}+\dfrac{9}{4}\right]-\dfrac{49}{4}\)
\(=\left(x+y+\dfrac{3}{2}\right)^2-\dfrac{49}{4}=\left(x+y+\dfrac{3}{2}-\dfrac{7}{2}\right)\left(x+y+\dfrac{3}{2}+\dfrac{7}{2}\right)=\left(x+y-2\right)\left(x+y+5\right)\)
4 tháng 9 2021
\(\left(x+y\right)^2+3\left(x+y\right)-10\)
\(=\left(x+y\right)^2+5\left(x+y\right)-2\left(x+y\right)-10\)
\(=\left(x+y+5\right)\left(x+y-2\right)\)
DN
1
12 tháng 9 2021
\(=x\left[x^2\left(x-y\right)^2-36y^2\right]\\ =x\left[x\left(x-y\right)-6y\right]\left[x\left(x-y\right)+6y\right]\\ =x\left(x^2-xy-6y\right)\left(x^2-xy+6y\right)\)
DN
3
2 tháng 9 2021
\(\left(x+y+z\right)^2+\left(x+y-z\right)^2-4z^2=\left(x+y+z\right)^2+\left(x+y-z-2z\right)\left(x+y-z+2z\right)=\left(x+y+z\right)^2+\left(x+y-3z\right)\left(x+y+z\right)=\left(x+y+z\right)\left(x+y+z+x+y-3z\right)=\left(x+y+z\right)\left(2x+2y-2z\right)=2\left(x+y+z\right)\left(x+y-z\right)\)
2 tháng 9 2021
Ta có:
(x + y + z)2 + (x + y – z)2 – 4z2
\(=\left(x+y-z\right)^2+\left(x+y-z\right)\left(x+y+3z\right)\)
\(=\left(x+y-z\right)\left(x+y+3z+x+y-z\right)\)
\(=2\left(x+y-z\right)\left(x+y+z\right)\)
NH
0
BM
1
23 tháng 9 2018
ab(x2+y2)+xy(a2+b2)
\(=abx^2+aby^2+a^2xy+b^2xy=\left(abx^2+a^2xy\right)+\left(aby^2+b^2xy\right).\)
\(=ax\left(bx+ay\right)+by\left(ay+bx\right)=\left(ax+by\right).\left(ay+bx\right)\)
\(\left(xy+1\right)^2-\left(x+y\right)^2=\left(xy+1-x-y\right)\left(xy+1+x+y\right)=\left[x\left(y-1\right)-\left(y-1\right)\right]\left[x\left(y+1\right)+\left(y+1\right)\right]=\left(x-1\right)\left(y-1\right)\left(x+1\right)\left(y+1\right)\)
\(\left(xy+1\right)^2-\left(x+y\right)^2\)
\(=\left(xy-x-y+1\right)\left(xy+1+x+y\right)\)
\(=\left(y-1\right)\left(x-1\right)\left(y+1\right)\left(x+1\right)\)