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A=\(x^3-2x^2+x\)
=x.(x2-2x+1)
=x(x-1)2
B=\(2x^2+4x+2-2y^2\)
=\(2\left(x^2+2x+1-y^2\right)\)
=\(2.\left[\left(x+1\right)^1-y^2\right]\)
=\(2\left(x+1-y\right)\left(x+1+y\right)\)
C=\(2xy-x^2-y^2+16\)
=\(-\left(-2xy+x^2+y^2-16\right)\)
=\(-\left[\left(x-y\right)^2-4^2\right]\)
=-(x-y-4)(x-y+4)
D=\(x^3+2x^2y+xy^2-9x\)
=\(x\left(x^2+2xy-y^2-9\right)\)
=\(x.\left[\left(x-y\right)^2-3^2\right]\)
=x.(x-y-3)(x-y+3)
E=\(2x-2y-x^2+2xy-y^2\)
\(=\left(2x-2y\right)-\left(x^2-2xy+y^2\right)\)
=\(2\left(x-y\right)-\left(x-y\right)\left(x-y\right)\)
=(x-y)(2x-2y-x+y)
=(x-y)(x+y)
a) \(\left(3x-5\right)\left(2x+3\right)-\left(2x-3\right)\left(3x+7\right)-2x\left(x-4\right)\)
\(=\left(6x^2-x-15\right)-\left(6x^2+5x-21\right)-\left(2x^2-8x\right)\)
\(=6x^2-x-15-6x^2-5x+21-2x^2+8x\)
\(=-2x^2+2x+6\)
\(=-2\left(x^2-x-3\right)\)
b) \(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^2-4\right)\left(x^2+4\right)\)
\(=\left(x^2+2\right)^2-\left(x^4-16\right)\)
\(=\left(x^4+4x^2+4\right)-\left(x^4-16\right)\)
\(=x^4+4x^2+4-x^4+16\)
\(=4x^2+20\)
\(=4\left(x^2+5\right)\)
c) \(\left(2x-y\right)^2-2\left(x+3y\right)^2-\left(1+3x\right)\left(3x-1\right)\)
\(=\left(4x^2-4xy+y^2\right)-2\left(x^2+6xy+9y^2\right)-\left(9x^2-1\right)\)
\(=4x^2-4xy+y^2-2x^2-16xy-18y^2-9x^2+1\)
\(=-7x^2-20xy-17y^2+1\)
d) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)\)
\(=\left(x^6-3x^4+3x^2-1\right)-\left(x^6-1\right)\)
\(=x^6-3x^4+3x^2-1-x^6+1\)
\(=-3x^4+3x^2\)
\(=-3x^2\left(x^2-1\right)\)
\(=-3x^2\left(x-1\right)\left(x+1\right)\)
e) \(\left(2x-1\right)^2-2\left(4x^2-1\right)+\left(2x+1\right)^2\)
\(=\left(2x-1\right)^2-2\left(2x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\)
\(=\left[\left(2x-1\right)-\left(2x+1\right)\right]^2\)
\(=\left(2x-1-2x-1\right)^2\)
\(=\left(-2\right)^2=4\)
g) \(\left(x-y+z\right)^2+\left(y-z\right)^2-2\left(x-y+z\right)\left(z-y\right)\)
\(=\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2\)
\(=\left(x-y+z+y+z\right)^2\)
\(=\left(x+2z\right)^2\)
h) \(\left(2x+3\right)^2+\left(2x+5\right)^2-\left(4x+6\right)\left(2x+5\right)\)
\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\)
\(=\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\)
\(=\left(2x+3-2x-5\right)^2\)
\(=\left(-2\right)^2=4\)
i) \(5x^2-\dfrac{10x^3+15x^2-5x}{-5x}-3\left(x+1\right)\)
\(=5x^2-\dfrac{-5x\left(-2x^2-3x+1\right)}{-5x}-3\left(x+1\right)\)
\(=5x^2-\left(-2x^2-3x+1\right)-3\left(x+1\right)\)
\(=5x^2+2x^2+3x-1-3x-3\)
\(=7x^2-4\)
Bài 1: Phân tích đa thức thành nhân tử
a) Ta có: \(8a^3-6a^2-1+3a\)
\(=\left[\left(2a\right)^3-1^3\right]-3a\left(2a-1\right)\)
\(=\left(2a-1\right)\left(4a^2+2a+1\right)-3a\left(2a-1\right)\)
\(=\left(2a-1\right)\left(4a^2+2a+1-3a\right)\)
\(=\left(2a-1\right)\left(4a^2-a+1\right)\)
b) Ta có: \(x^3-2x^2y+xy^2-9x\)
\(=x\left(x^2-2xy+y^2-9\right)\)
\(=x\left[\left(x^2-2xy+y^2\right)-9\right]\)
\(=x\left[\left(x-y\right)^2-3^2\right]\)
\(=x\left(x-y-3\right)\left(x-y+3\right)\)
c) Ta có: \(5x^2-45\)
\(=5\left(x^2-9\right)\)
\(=5\left(x-3\right)\left(x+3\right)\)
d) Ta có: \(2x^3-4x^2+2x\)
\(=x\left(2x^2-4x+2\right)\)
\(=x\left(2x^2-2x-2x+2\right)\)
\(=x\left[2x\left(x-1\right)-2\left(x-1\right)\right]\)
\(=x\left(x-1\right)\left(2x-2\right)\)
\(=2x\left(x-1\right)^2\)
e) Ta có: \(6x\left(3x-2\right)-12\left(2-3x\right)\)
\(=6x\left(3x-2\right)+12\left(3x-2\right)\)
\(=\left(3x-2\right)\left(6x+12\right)\)
\(=6\left(3x-2\right)\left(x+2\right)\)
f) Ta có: \(4x^2-8xy+4y^2-10\)
\(=\left(2x\right)^2-2\cdot2x\cdot2y+\left(2y\right)^2-10\)
\(=\left(2x-2y\right)^2-10\)
\(=\left(2x-2y-\sqrt{10}\right)\left(2x-2y+\sqrt{10}\right)\)
g) Ta có: \(2x^2-8x+8\)
\(=2\left(x^2-4x+4\right)\)
\(=2\left(x-2\right)^2\)
h) Ta có: \(\left(2x+1\right)^2-\left(x-1\right)^2\)
\(=\left[\left(2x+1\right)-\left(x-1\right)\right]\left[\left(2x+1\right)+\left(x-1\right)\right]\)
\(=\left(2x+1-x+1\right)\left(2x+1+x-1\right)\)
\(=3x\left(x+2\right)\)
\(e,-5x+x^2-14\)
\(=x^2+2x-7x-14\)
\(=x\left(x+2\right)-7\left(x+2\right)\)
\(=\left(x+2\right)\left(x-7\right)\)
\(f,x^3+8+6x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+2x+4\right)+6x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+8x+4\right)\)
\(g,15x^2-7xy-2y^2\)
\(=15x^2+3xy-10xy-2y^2\)
\(=3\left(5x+y\right)-2y\left(5x+y\right)\)
\(=\left(5x+y\right)\left(3-2y\right)\)
\(h,3x^2-16x+5\)
\(=3x^2-x-15x+5\)
\(=x\left(3x-1\right)+5\left(3x-1\right)\)
\(=\left(3x-1\right)\left(x+5\right)\)
\(a,x^3+2x^2y+xy^2=x\left(x^2+2xy+y^2\right)\)
\(=x\left(x+y\right)^2\)
\(b,4x^2-9y^2+4x-6y\)
\(=4x^2+4x+1-\left(9y^2+6y+1\right)\)
\(=\left(2x+1\right)^2-\left(3y+1\right)^2\)
\(=\left(2x-3y\right)\left(2x+3y+2\right)\)
\(c,-x^2+5x+2xy-5y-y^2\)
\(=-\left(x^2-2xy+y^2\right)+5\left(x-y\right)\)
\(=-\left(x-y\right)^2+5\left(x-y\right)\)
\(=\left(x-y\right)\left(y-x+5\right)\)
\(d,x^2+4x-12\)
\(=x^2-2x+6x-12\)
\(=x\left(x-2\right)+6\left(x-2\right)\)
\(=\left(x-2\right)\left(x+6\right)\)
Dài dữ trời :V Về sau gửi từng bài một thôi, nhìn hoa mắt quá @@
B1: Phân tích thành nhân tử:
a) \(6x^2+9x=3x\left(2x+3\right)\)
b) \(4x^2+8x=4x\left(x+2\right)\)
c) \(5x^2+10x=5x\left(x+2\right)\)
d) \(2x^2-8x=2x\left(x-4\right)\)
e) \(5x-15y=5\left(x-3y\right)\)
f) \(x\left(x^2-1\right)+3\left(x^2-1\right)=\left(x^2-1\right)\left(x+3\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x+3\right)\)
g) \(x^2-2x+1-4y^2=\left(x-1\right)^2-4y^2\)
\(=\left(x-1-2y\right)\left(x-1+2y\right)\)
h) \(x^2-100=\left(x-10\right)\left(x+10\right)\)
i) \(9x^2-18x+9=\left(3x-3\right)^2\)
k) \(x^3-8=\left(x-2\right)\left(x^2+2x+4\right)\)
l) \(x^2+6xy^2+9y^4=\left(x+3y\right)^2\)
m) \(4xy-4x^2-y^2=-\left(4x^2-4xy+y^2\right)\)
\(=-\left(2x-y\right)^2\)
n) \(\left(x-15\right)^2-16=\left(x-15-16\right)\left(x-15+16\right)\)
\(=\left(x-31\right)\left(x+1\right)\)
o) \(25-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3+x\right)\)
\(=\left(2+x\right)\left(8+x\right)\)
p) \(\left(7x-4\right)^2-\left(2x+1\right)^2\)
\(=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)\)
\(=\left(5x-5\right)\left(9x-3\right)\)
Bài 1 :
a ) \(6x^2+9x=3x\left(x+3\right)\)
b ) \(4x^2+8x=4x\left(x+2\right)\)
c ) \(5x^2+10x=5x\left(x+2\right)\)
d ) \(2x^2-8x=2x\left(x-4\right)\)
e ) \(5x-15y=5\left(x-3y\right)\)
f ) \(x\left(x^2-1\right)+3\left(x^2-1\right)=\left(x^2-1\right)\left(x+3\right)\)
g ) \(x^2-2x+1-4y^2=\left(x-1\right)^2-\left(2y\right)^2=\left(x-1-2y\right)\left(x-1+2y\right)\)
h ) \(x^2-100=x^2-10^2=\left(x-10\right)\left(x+10\right)\)
i ) \(9x^2-18x+9=\left(3x-3\right)^2\)
k ) \(x^3-8=\left(x-2\right)\left(x^2+2x+2^2\right)\)
l ) \(x^2+6xy^2+9y^4=\left(x+3y^2\right)^2\)
m ) \(4xy-4x^2-y^2=-\left(2x-y\right)^2\)
n ) \(\left(x-15\right)^2=x^2-30x+15^2\)
o ) \(25-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3-x\right)=\left(2+x\right)\left(8-x\right)\)
p ) \(\left(7x-4\right)^2-\left(2x+1\right)^2=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)=\left(5x-5\right)\left(9x-3\right)\)
Bài 2 :
a ) \(3x^3-6x^2+3x^2y-6xy=3x\left(x^2-2x+xy-2y\right)\)
b ) \(x^2-2x+xy-2y=x\left(x-2\right)+y\left(x-2\right)=\left(x-2\right)\left(x+y\right)\)
c ) \(2x+x^2-2y-2xy=......................\)
d ) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
e ) \(x^2+y^2-2xy-4=\left(x-y\right)^2-2^2=\left(x-y-2\right)\left(x-y+2\right)\)
f )\(2xy-x^2-y^2+9=-\left(x-y\right)^2+9=3^2-\left(x-y\right)^2=\left(3-x+y\right)\left(3+x-y\right)\)
a, 3x - 3y = 3( x- y )
b, x2 - x =x(x - 1)
c, 3(x - y) - 5x(y - x)
= 3(x - y) + 5x(x - y)
= ( x - y)(3 + 5x)
d, x(y - 1) - y(y - 1)
= (x - y)(y - 1)
e, 10x(x - y)-8y( y - x)
= 10x(x - y) + 8y(x - y)
= (10y + 8x)(x - y)
f, 2x2 +5x3 +xy
= x(2x + 5x2 + y)
g, 14x2y - 21xy2 +28x2y2
= 7xy(2x - 3y + 4xy)
h, x2 - 3x + 2
= x2 - x - 2x + 2
= x(x - 1)- 2(x - 1)
= (x - 2)(x - 1)
i, x2 - x - 6
x2 + 2x - 3x - 6
x(x + 2) - 3(x + 2)
(x + 2)(x - 3)
k, x2 + 5x+6
= x2 - x + 6x + 6
=x(x - 1) + 6(x + 1)
= x(x - 1) - 6(x - 1)
= (x - 6)(x - 1)
l,x2 - 4x + 3
= x2 - x - 3x + 3
= x(x - 1) - 3(x - 1)
= (x - 3)(x - 1)
m, x2 + 5x +4
= x2 + x + 4x + 4
= x(x + 1) + 4(x + 1)
= (x + 4)(x + 1)
Bài 1: Phân tích đa thức thành nhân tử
a) Ta có: \(16x^2-y^2+6y-9\)
\(=16x^2-\left(y^2-6y+9\right)\)
\(=\left(4x\right)^2-\left(y-3\right)^2\)
\(=\left[4x-\left(y-3\right)\right]\left[4x+\left(y-3\right)\right]\)
\(=\left(4x-y+3\right)\left(4x+y-3\right)\)
b) Ta có: \(a^2-16a^2b^2+b^2+2ab\)
\(=\left(a^2+2ab+b^2\right)-\left(4ab\right)^2\)
\(=\left(a+b\right)^2-\left(4ab\right)^2\)
\(=\left(a+b-4ab\right)\left(a+b+4ab\right)\)
c) Ta có: \(x^3-6x^2-9x\)
\(=x\left(x^2-6x-9\right)\)
d) Ta có: \(mx^2+my^2-nx^2-ny^2\)
\(=m\left(x^2+y^2\right)-n\left(x^2+y^2\right)\)
\(=\left(x^2+y^2\right)\left(m-n\right)\)
e) Ta có: \(a^3+b^3+a^2c+b^2c-abc\)
\(=\left(a+b\right)\left(a^2-ab+b^2\right)+c\left(a^2-ab+b^2\right)\)
\(=\left(a^2-ab+b^2\right)\left(a+b+c\right)\)
f) Ta có: \(4x^2-y^2-4x+1\)
\(=\left(4x^2-4x+1\right)-y^2\)
\(=\left(2x-1\right)^2-y^2\)
\(=\left(2x-1-y\right)\left(2x-1+y\right)\)
g) Ta có: \(\left(2x+3\right)^2+5\cdot\left(2x+3\right)\)
\(=\left(2x+3\right)\left(2x+3+5\right)\)
\(=\left(2x+3\right)\left(2x+8\right)\)
\(=2\left(2x+3\right)\left(x+4\right)\)
h) Ta có: \(3x^2-10x-8\)
\(=3x^2-12x+2x-8\)
\(=3x\left(x-4\right)+2\left(x-4\right)\)
\(=\left(x-4\right)\left(3x+2\right)\)
cảm ơn nhiều ạ :)))