Câu 1
a,(2x²-3xy+x³)
b,(24x⁵-12x⁴+6x²):6x²
c,(2x+3)²+(2x-3)²-(2x+3)(4x-6)+xy
d,(4x²+4x+1):2x+1
Câu 2: Phân tích đa thức thành nhân tử
a,x²+x-y²+y
b,3x²+3y²-6xy-12
c,3x+3y-x²-2xy-y²
d,x³-x+3x²y+3xy²-y+y³
Câu 3: Phân tích đa thức thành nhân tử
a,x²-y²-2x-2y
b,18m²-36mn+18n²-72p²
Câu 4:
a,Rút gọn biểu thức A=x²(x+y)+y²(x+y)+2x²y+2xy²
b, Làm tính chia (x³+4x²-x-4):(x+1)
Câu 5: Tìm x biết
x(3x+2)+(x+1)²-(2x-5)(2x+5)=-12
1.a)Lỗi...
b)\(\left(24x^5-12x^4+6x^2\right):6x^2=6x^2\left(4x^3-2x^2+x\right):6x^2=4x^3-2x^2+x\)
c)\(\left(2x+3\right)^2+\left(2x-3\right)^2-\left(2x+3\right)\left(4x-6\right)+xy\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x-3\right)+\left(2x-3\right)^2+xy\)
\(=\left(2x+3-2x+3\right)^2+xy\)
\(=36+xy\)
d)\(\left(4x^2+4x+1\right):\left(2x+1\right)=\left(2x+1\right)^2:\left(2x+1\right)=2x+1\)
2.a)\(x^2+x-y^2+y=\left(x+y\right)\left(x-y\right)+\left(x+y\right)=\left(x+y\right)\left(x-y+1\right)\)
b)\(3x^2+3y^2-6xy-12=3\left(x^2-2xy+y^2-4\right)=3\left[\left(x-y\right)^2-4\right]=3\left(x-y+2\right)\left(x-y-2\right)\)
c)\(3x+3y-x^2-2xy-y^2=3\left(x+y\right)-\left(x+y\right)^2=\left(x+y\right)\left(3-x-y\right)\)
d)\(x^3-x+3x^2y+3xy^2-y+y^3=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)
3.a)\(x^2-y^2-2x-2y=\left(x+y\right)\left(x-y\right)-2\left(x+y\right)=\left(x+y\right)\left(x-y-2\right)\)
b)\(18m^2-36mn+18n^2-72p^2=18\left(m^2-2mn+n^2-4\right)=18\left[\left(m-n\right)^2-4\right]=18\left(m-n+2\right)\left(m-n-2\right)\)
4.a)\(A=x^2\left(x+y\right)+y^2\left(x+y\right)+2x^2y+2xy^2\)
\(=\left(x+y\right)\left(x^2+y^2\right)+2xy\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2\right)\)
\(=\left(x+y\right)\left(x+y\right)^2=\left(x+y\right)^3\)
b)\(\left(x^3+4x^2-x-4\right):\left(x+1\right)\)
\(=\left[x^2\left(x+4\right)-\left(x+4\right)\right]:\left(x+1\right)\)
\(=\left(x+4\right)\left(x^2-1\right):\left(x+1\right)\)
\(=\left(x+4\right)\left(x+1\right)\left(x-1\right):\left(x+1\right)\)
\(=\left(x+4\right)\left(x-1\right)\)
5.\(x\left(3x+2\right)+\left(x+1\right)^2-\left(2x-5\right)\left(2x+5\right)=-12\)
\(\Leftrightarrow3x^2+2x+x^2+2x+1-\left(4x^2-25\right)=-12\)
\(\Leftrightarrow4x^2+4x+1-4x^2+25=-12\)
\(\Leftrightarrow4x=-38\)
\(\Leftrightarrow x=-\frac{19}{2}\)
Vậy pt có nghiệm duy nhất là \(x=-\frac{19}{2}\)
