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\(a,-x-y^2+x^2-y\)
\(=-\left(x+y\right)+x^2-y^2\)
\(=-\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y-1\right)\)
\(b,x^2-y^2-2xy+y^2\)
\(=\left(x-y\right)^2-y^2\)
\(=\left(x-y-y\right)\left(x-y+y\right)=\left(x-2y\right)x\)
\(d,x^6-y^6\)
\(=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
a) x2+ 4x+4-y2
=(x2+2.x.2+22)-y2
=(x+2)2-y2
=(x+2+y)(x+2-y)
b)(x2-2xy+y2)-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
\(x^2+4x+4-y^2\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right)\left(x+2+y\right)\)
hk tốt
^^
x6+3x4y2-8x3y3+3x2y4+y6= x6+3x4y2+3x2y4+y6-8x3y3=(x2+y2)3-(2xy)3
= (x2+y2-2xy)[(x2+y2)2+2xy(x2+y2)+(2xy)2]= (x-y)2(x4+6x2y2+y4+2x3y+2xy3)
(x2+y2-5)2-4x2y2-16xy-16=(x2+y2-5)2-(4x2y2+16xy+16)=(x2+y2-5)2-(2xy+4)2
=(x2+y2-5+2xy+4)(x2+y2-5-2xy-4)=(x2+2xy+y2-1)(x2-2xy+y2-9)=[(x+y)2-1][(x-y)2-32]=(x+y-1)(x+y+1)(x-y-3)(x-y+3)
x4+324=x4+36x2+324-36x2=(x2+18)2-(6x)2=(x2+18-6x)(x2+18+6x)
Bài 8:
b. 1+8x6y3 = 13+23(x2)3y3 = 13+(2x2y)3
= (1+2x2y)(1-2x2y+4x4y2)
e. 27x3+\(\dfrac{y^3}{8}\)\(=\left(3x\right)^3+\left(\dfrac{y}{2}\right)^3\)
= (3x+\(\dfrac{y}{2}\))(9x2-\(\dfrac{3xy}{2}\)+\(\dfrac{y^2}{4}\))
Bài 9:
c. 1- 9x +27x2 -27x3 = 13-3.12.3x+3.(3x)2-(3x)3
= (1-3x)3
d. x3+\(\dfrac{3}{2}x^2\)+\(\dfrac{3}{4}x+\dfrac{1}{8}\) = x3+\(3x^2.\dfrac{1}{2}\)+\(3x.\dfrac{1}{4}+\left(\dfrac{1}{2}\right)^3\)
= (x+\(\dfrac{1}{2}\))3
f. x2 - 2xy +y2 -4m2 +4m.n - n2 = (x2 - 2xy +y2)-((2m)2 -2.2m.n + n2)
= (x-y)2-(2m-n)2 = (x-y-2m+n)(x-y+2m-n)
a) x2 - y2 + 4x + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y )( x + 2 + y )
b) x2 - 2xy + y2 - 1
= ( x2 - 2xy + y2 ) - 1
= ( x - y )2 - 12
= ( x - y - 1 )( x - y + 1 )
c) x2 - 2xy + y2 - 4
= ( x2 - 2xy + y2 ) - 4
= ( x - y )2 - 22
= ( x - y - 2 )( x - y + 2 )
d) x2 - 2xy + y2 - z2
= ( x2 - 2xy + y2 ) - z2
= ( x - y )2 - z2
= ( x - y - z )( x - y + z )
e) 25 - x2 + 4xy - 4y2
= 25 - ( x2 - 4xy + 4y2 )
= 52 - ( x - 2y )2
= ( 5 - x + 2y )( 5 + x - 2y )
f) x2 + y2 - 2xy - 4z2
= ( x2 - 2xy + y2 ) - 4z2
= ( x - y )2 - ( 2z )2
= ( x - y - 2z )( x - y + 2z )
a) 10x(x-y)-6y(y-x)=10x(x-y)+6y(x-y)=(10x+6y)(x-y)
b) \(x^2-25-2xy+y^2=x^2-2xy+y^2-25=\left(x-y\right)^2-25\)
\(=\left(x-y+5\right)\left(x-y-5\right)\)
c) \(x^2-5x+5y-y^2=\left(x^2-y^2\right)-\left(5x-5y\right)\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)=\left(x+y-5\right)\left(x-y\right)\)
d)\(x^2+4x+3=x^2+x+3x+3=x\left(x+1\right)+3\left(x+1\right)\)\(=\left(x+3\right)\left(x+1\right)\)
e)\(x^2-4x-5=x^2-5x+x-5=x\left(x-5\right)+\left(x-5\right)\)\(=\left(x+1\right)\left(x-5\right)\)
\(1,4x^4+4x^2y^2-8y^4\)
\(=4\left(x^4+x^2y^2-y^4-y^4\right)\)
\(=4\left[\left(x^4-y^4\right)+\left(x^2y^2-y^4\right)\right]\)
\(=4\left[\left(x^2+y^2\right)\left(x^2-y^2\right)+y^2\left(x^2-y^2\right)\right]\)
\(=4\left(x^2-y^2\right)\left(x^2+y^2+y^2\right)\)
\(=4\left(x-y\right)\left(x+y\right)\left(x^2+2y^2\right)\)
\(2,12x^2y-18xy^2-30y^3\)
\(=6y\left(2x^2-3xy-5y^2\right)\)
\(=6y\left[\left(2x^2+2xy\right)-\left(5xy+5y^2\right)\right]\)
\(=6y\left[2x\left(x+y\right)-5y\left(x+y\right)\right]\)
\(=6y\left(x+y\right)\left(2x-5y\right)\)
b) \(5x-5y+ax-ay \)
\(=\left(5x-5y\right)+\left(ax-ay\right)\)
\(=5.\left(x-y\right)+a.\left(x-y\right)\)
\(=\left(x-y\right)\left(5+a\right)\)
c) \(a^3-a^2x-ay+xy\)
\(=\left(a^3-a^2x\right)-\left(ay-xy\right)\)
\(=a^2\left(a-x\right)-y\left(a-x\right)\)
\(=\left(a-x\right)\left(a^2-y\right)\)
a) \(-x-y^2+x^2-y=-\left(x+y\right)+\left(x^2-y^2\right)=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right).\left(x-y-1\right)\)
b)
\(x^2-y^2-2xy+y^2=\left(x^2-2xy+y^2\right)-y^2=\left(x-y\right)^2-y^2=\left(x-y+y\right)\left(x-y-y\right)=x.\left(x-2y\right)\)
c) \(x^2-y^2+4-4x=\left(x^2-4x+4\right)-y^2=\left(x^2-2.x.2+2^2\right)-y^2=\left(x-2\right)^2-y^2=\left(x-2+y\right).\left(x-2-y\right)\)
d) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3+y^3\right)\left(x^3-y^3\right)=\left(x+y\right)\left(x^2-xy+y^2\right).\left(x-y\right)\left(x^2+xy+y^2\right)\)
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