Giải:
\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left[\left(x-y+4\right)-\left(2x+3y-1\right)\right]\left[\left(x-y+4\right)+\left(2x+3y-1\right)\right]\)
\(=\left(x-y+4-2x-3y+1\right)\left(x-y+4+2x+3y-1\right)\)
\(=\left(5-x-4y\right)\left(3+3x+2y\right)\)
Vậy ...
Phân tích các đa thức sau thành nhân tử
a) \(3x^3y^3 - 15x^2y^2\)
b) \(5x^3y^2 - 25x^2y^3 + 40xy^4\)
c) \(-4x^3y + 6x^2y^2 - 8x^4y^3\)
d) \(a^3x^2y - \)\(\frac{5}{2}a^3x^4+\frac{2}{3}a^4x^2y\)
e) \(a\left(x+1\right)-b\left(x+1\right)\)
f) \(2x\left(x-5y\right)+8y\left(5y-x\right)\)
g) \(a\left(x^2+1\right)+b\left(-1-x^2\right)-c\left(x^2+1\right)\)
h) \(9\left(x-y\right)^2-27\left(y-x\right)^3\)
M.n làm ơn giúp mink nha, cảm ơn!!!!
Chứng minh rằng với mọi số nguyên x,y thì:
a) \(x\left(x^2-2x\right)+\left(x-2x\right)\) chia hết cho x - 2
b) \(x^3y^2-3yx^2+xy\) chia hết cho xy
c) \(x^3y^2-3x^2y^3+xy^2\) chia hết cho \(x^2-3xy+1\)
Tìm x:
b, \(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x+7\right)\left(x-7\right)=0\)
c, \(\left(x-2\right)^3-\left(x-4\right)\left(x^2+4x+16\right)+6\left(x+1\right)^2=49\)
d, \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)
1. PHÂN TÍCH ĐA THỨC THÀNH NHÂN TỬ
a) \(2x\left(x+1\right)+2\left(x+1\right)\)
b) \(\left(2x+1\right)^2-\left(x-1\right)^2\)
c) \(25\left(x-y\right)^2-16\left(x+y\right)^2\)
d) \(x^2-2xy+y^2-xz+yz\)
e) \(x^2-y^2-x+y\)
f) \(a^3x-ab+b-x\)
g) \(x^2+2x-4y^2-4y\)
h) \(xy-4+2x-2y\)
i) \(x^3-x^2y-xy^2+y^3\)
1 . Tìm x biết rằng :
a) \(2\left(2x-1\right)^2-\left(x-3\right)^2=\left(x+1\right)\left(7x+2\right)\)
b) \(\left(x+1\right)^3=4x+4\)
Tìm x :
a) \(\left(4x^3+2x^2+199x\right):x=2005\)
b) \(2\left(x-1\right)^2+3\left(x-2\right)^2=5\left(x+2\right)\left(x+1\right)+4\)
Phân tích đa thức thành nhân tử:
1). (x - 3)(x - 1) - 3(x - 3)
2). (6x + 3) - (2x - 5)(2x + 1)
3). (x - 1)(2x + 1) + 3(x - 1)(x + 2)(2x + 1)
4). (3x - 2)(4x - 3) - (2 - 3x)(x - 1) - 2(3x - 2)(x + 1)
5). \(\left(x-5\right)^2+\left(x+5\right)\left(x-5\right)-\left(5-x\right)\left(2x+1\right)\)
6). (a - b)(a + 2ab) - (b - a)(2a - b) - (a - b)(a + 3b)
Tìm x :
a) \(4x^2-8x=0\)
b) \(\left(x+5\right)-3x\left(x+5\right)=0\)
c) \(2x\left(x-4\right)^2-\left(x-4\right)=0\)
d) \(3x\left(x-1\right)+\left(1-x\right)^2=0\)
e) \(5x\left(x-9\right)^2-\left(9-x\right)^3=0\)
Tính giá trị của biểu thức: \(\left(x-y\right)\left(2x+y+z\right)-\left(x-y\right)\left(x+z\right)-\left(x^2-y^2\right)\) với \(x=2015,y=0,000125,z=\sqrt{2016}\)
