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\(a,=15x^4-12x^3+9x^2\\ b,=-15x^3y^2+25x^2y^2-5xy^3\\ c,=5x^3-19x^2+12x\\ d,=3x^3+xy^2+5x^2y-9x^2y-3y^3-15xy^2\\ =3x^3-3y^3-14xy^2-4x^2y\)
Bài 2:
a: \(x^2+5x-6=\left(x+6\right)\left(x-1\right)\)
b: \(5x^2+5xy-x-y\)
\(=5x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(5x-1\right)\)
c:\(-6x^2+7x-2\)
\(=-6x^2+3x+4x-2\)
\(=-3x\left(2x-1\right)+2\left(2x-1\right)\)
\(=\left(2x-1\right)\left(-3x+2\right)\)
1.
a) \(=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)
b) \(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
c) \(=5\left[\left(x^2-2xy+y^2\right)-4z^2\right]=5\left[\left(x-y\right)^2-4z^2\right]\)
\(=5\left(x-y-2z\right)\left(x-y+2z\right)\)
2.
a) \(=x\left(x+2\right)+3\left(x+2\right)=\left(x+2\right)\left(x+3\right)\)
b) \(=5x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(5x-1\right)\)
c) \(=-\left[3x\left(2x-1\right)-2\left(2x-1\right)\right]=-\left(2x-1\right)\left(3x-2\right)\)
3.
b) \(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
c) \(=-\left[5x\left(x-3\right)-1\left(x-3\right)\right]=-\left(x-3\right)\left(5x-1\right)\)
4.
a) \(\Rightarrow\left(x-1\right)\left(5x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{1}{5}\end{matrix}\right.\)
b) \(\Rightarrow2\left(x+5\right)-x\left(x+5\right)=0\)
\(\Rightarrow\left(x+5\right)\left(2-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)
1.\(=5\left(x^2-2xy+y^2-4z^2\right)=5\left[\left(x+y\right)^2-\left(2z\right)^2\right]=5\left(x+y-2z\right)\left(x+y+2z\right)\)
2. \(=\left(-5x^2+15x\right)+\left(x-3\right)=-5x\left(x-3\right)+\left(x-3\right)=\left(1-5x\right)\left(x-3\right)\)
3. \(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\)
4.\(=3\left(x^2-2xy+y^2-4z^2\right)=3\left[\left(x-y\right)^2-\left(2z\right)^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\)
5. \(=\left(x^2+x\right)+\left(3x+3\right)=x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(x+3\right)\)
6. \(=\left(x^2-2x+1\right)\left(x^2+2x+1\right)=\left(x-1\right)^2\left(x+1\right)^2\)
7. \(=\left(x^2+x\right)-\left(5x+5\right)=x\left(x+1\right)-5\left(x+1\right)=\left(x-5\right)\left(x+1\right)\)
\(1,=5\left[\left(x-y\right)^2-4z^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\\ 2,=-5x^2+15x+x-3=\left(x-3\right)\left(1-5x\right)\\ 3,=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x-y\right)\left(x+y-5\right)\\ 4,=3\left[\left(x-y\right)^2-4z^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\\ 5,=x^2+x+3x+3=\left(x+3\right)\left(x+1\right)\\ 6,=\left(x^2+2x+1\right)\left(x^2-2x+1\right)=\left(x-1\right)^2\left(x+1\right)^2\\ 7,=x^2+x-5x-5=\left(x+1\right)\left(x-5\right)\)
a, \(15^4-12x^3+9x^2\)
b,\(-15x^3y^2+25x^2y^2-5xy^3\)
c, \(5x^3-19x^2+12x\)
d,
x3+xy2+5x2y−9x2y−3y3−15xy2=3x3−3y3−14xy2−4x2y
\(a,=15x^4-12x^3+9x^2\\ b,=-15x^3y^2+25x^2y^2-5xy^3\\ c,=5x^3-15x^2-4x^2+12x=5x^3-19x^2+12x\\ d,=3x^3+xy^2+5x^2y-9x^2y-3y^3-15xy^2=3x^3-14xy^2-4x^2y-3y^3\)
Bài 1:
a: \(x\left(x+y\right)+5y-x^2\)
\(=x^2+xy+5y-x^2\)
=xy+5y
b: \(\left(x-2\right)\left(y+1\right)-xy+4\)
\(=xy+x-2y-2-xy+4\)
=-2y+x+2
c: \(\dfrac{\left(4x^2y+12xy^2-8xy\right)}{2xy}\)
\(=\dfrac{2xy\cdot2x+2xy\cdot6y-2xy\cdot4}{2xy}\)
=2x+6y-4
d: \(\left(x-4\right)^2+8x-7\)
\(=x^2-8x+16+8x-7\)
\(=x^2+9\)
1) x³ + 2x² + x
= x(x² + 2x + 1)
= x(x + 1)²
2) 5x³ - 10x² + 5x
= 5x(x² - 2x + 1)
= 5x(x - 1)²
3) 8x²y - 8xy + 2x
= 2x(4xy - 4y + 1)
5) 2x² + 5x³ + x²y
= x²(2 + 5x + y)
6) 4x²y - 8xy² + 18x²y²
= 2xy(2x - 4y + 9xy)
Nếu ol thì tham khảo nah nguoiemtinhthong.
1.1
2x2+5x−1=7x3−1−−−−−√2x2+5x−1=7x3−1
⇔2(x2+x+1)+3(x−1)−7(x−1)(x2+x+1)−−−−−−−−−−−−−−−√(1)⇔2(x2+x+1)+3(x−1)−7(x−1)(x2+x+1)(1)
Đặt a=x−1−−−−−√;b=x2+x+1−−−−−−−−√;a≥0;b>0a=x−1;b=x2+x+1;a≥0;b>0
pt (1) trở thành 3a2+2b2−7ab=03a2+2b2−7ab=0
a=2ba=2b v a=13ba=13b
Các bạn tự giải quyết tiếp nhé.
1.2
TXĐ D=[1;+∞)D=[1;+∞)
đặt a=x−1−−−−−√4;b=x+1−−−−−√4;a,b≥0a=x−14;b=x+14;a,b≥0
pt (2) trở thành 3a2+2b2−5ab=03a2+2b2−5ab=0
⇔a=b⇔a=b v a=23ba=23b
...
1.3
D=[3;+∞)D=[3;+∞)
Đặt a=x2+4x−5−−−−−−−−−√;b=x−3−−−−−√;a,b≥0a=x2+4x−5;b=x−3;a,b≥0
pt (3) trở thành 3a+b=11a2−19b2−−−−−−−−−√3a+b=11a2−19b2
⇔2a2−6ab−20b2=0⇔2a2−6ab−20b2=0
⇒a=5b⇒a=5b
...
1.4
ĐK
⇔2x2−2x+2=3(x−2)x(x+1)−−−−−−−−−−−−√2x2−2x+2=3(x−2)x(x+1)
⇔(x2−2x)+2(x+1)=3(x2−2x)(x+1)−−−−−−−−−−−−−√2(x2−2x)+2(x+1)=3(x2−2x)(x+1)
Đặt x2−2x−−−−−−√=ax2−2x=a; x+1−−−−−√=bx+1=b (a;b\geq0)
⇔2a2+2b2=3ab
1.5
Đặt 4x2−4x−10=t4x2−4x−10=t (t \geq 0)
⇔t=t+4x2−2x−−−−−−−−−−√t=t+4x2−2x
⇔t2−t−4x2+2x=0t2−t−4x2+2x=0
Δ=1−4(2x−4x2)=(4x−1)2Δ=1−4(2x−4x2)=(4x−1)2
⇒t=1−2xt=1−2x hoặc t=2xt=2x
1.1
2.2+5.-1=7.3-1-----v2.2+5.-1=7.3-1
2(.2+x+1)+3(x-1)
3a+b=11a2-19b2
tóm tắt
a) \(\left(3x^2y-11x^2-5y\right)\left(8xy-5x+6\right)\)
\(=3x^2y\left(8xy-5x+6\right)-11x^2\left(8xy-5x+6\right)-5y\left(8xy-5x+6\right)\)
\(=24x^3y^2-15x^3y+18x^2y-88x^3y+55x^3-66x^2-40xy^2+25xy-30y\)
\(=24x^3y^2-103x^3y+18x^2y+55x^3-66x^2-40xy^2+25xy-30y\)
b) \(\left(-4x^2y-5x^2+3y^3\right)\left(2x^2-xy+3y^2\right)\)
\(=-4x^2y\left(2x^2-xy+3y^2\right)-5x^2\left(2x^2-xy+3y^2\right)+3y^3\left(2x^2-xy+3y^2\right)\)
\(=-8x^4y+4x^3y^2-12x^2y^3-10x^4+5x^3y-15x^2y^2+6x^2y^3-3xy^4+9y^5\)
\(=-8x^4y+4x^3y^2-6x^2y^3-10x^4+5x^3y-15x^2y^2-3xy^4+9y^5\)
P/s: Ko chắc ạ!