Giúp minh với,cần...
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Giúp minh với,cần gấp
a)\(ax-bx+ab-x^2\)
b)\(x^2-y^2+4x+4\)
c)\(ax+ay-3x-3y\)
d)\(x^3+x^2+x+1\)
e)\(x^3-3x^2+3x-9\)
f)\(x^2+ab+ax+bx\)
g)\(xy+1+x+y\)
h)\(9-x^2-2xy-y^2\)
i)\(x^2-2xy+y^2-1\)
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B
17 tháng 7 2019
\(a,xy+1-x-y\)
\(=\left(xy-y\right)+\left(1-x\right)\)
\(=y\left(x-1\right)- \left(x-1\right)\)
\(=\left(x-1\right)\left(y-1\right)\)
\(b,ax+ay-3x-3y\)
\(=a\left(x+y\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(a-3\right)\)
\(c,x^3-2x^2+2x-4\)
\(=x^2\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x^2+2\right)\left(x-2\right)\)
\(d,x^2+ab+ax+bx\)
\(=\left(x^2+ax\right)+\left(ab+bx\right)\)
\(=x\left(a+x\right)+b\left(a+x\right)\)
\(=\left(a+x\right)\left(b+x\right)\)
\(e,16-x^2+2xy-y^2\)
\(=4^2-\left(x^2-2xy+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
8 tháng 9 2020
A = xy + y - 2x - 2
= y( x + 1 ) - 2( x + 1 )
= ( x + 1 )( y - 2 )
B = x2 - 3x + xy - 3y
= x( x - 3 ) + y( x - 3 )
= ( x - 3 )( x + y )
C = 3x2 - 3xy - 5x + 5y
= 3x( x - y ) - 5( x - y )
= ( x - y )( 3x - 5 )
D = xy + 1 + x + y
= y( x + 1 ) + ( x + 1 )
= ( x + 1 )( y + 1 )
E = ax - bx + ab - x2
= ( ax - x2 ) + ( ab - bx )
= x( a - x ) + b( a - x )
= ( a - x )( x + b )
F = x2 + ab + ax + bx
= ( ax + x2 ) + ( ab + bx )
= x( a + x ) + b( a + x )
= ( a + x )( x + b )
G = a3 - a2x - ay + xy
= a2( a - x ) - y( a - x )
= ( a - x )( a2 - y )
Bonus : = ( a - x )[ a2 - ( √y )2 ]
= ( a - x )( a - √y )( a + √y )
H = 2xy + 3z + 6y + xz
= ( 6y + 2xy ) + ( 3z + xz )
= 2y( 3 + x ) + z( 3 + x )
= ( 3 + x )( 2y + z )
XO
8 tháng 9 2020
A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1
B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)
C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)
D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)
E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)
F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)
G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)
H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)
17 tháng 7 2019
a) \(xy+1-x-y\)
\(=x\left(y-1\right)-\left(y-1\right)\)
\(=\left(y-1\right)\left(x-1\right)\)
b) \(ax+ay-3x-3y\)
\(=a\left(x+y\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(a-3\right)\)
c) \(x^3-2x^2+2x-4\)
\(=x^2\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2\right)\)
d) \(x^2+ab+ax+bx\)
\(=x\left(b+x\right)+a\left(b+x\right)\)
\(=\left(b+x\right)\left(a+x\right)\)
e) \(16-x^2+2xy-y^2\)
\(=16-\left(x^2-2xy+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
f) \(ax^2+ax-bx^2-bx-a+b\)
\(=\left(ax^2+ax-a\right)-\left(bx^2+bx-b\right)\)
\(=a\left(x^2+x-1\right)-b\left(x^2+x-1\right)\)
\(=\left(x^2+x-1\right)\left(a-b\right)\)
1 tháng 8 2019
a) \(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2\)
\(=\left(x-3-y\right)\left(x-3+y\right)\)
1 tháng 8 2019
b) \(9-x^2+2xy-y^2\)
\(=9-\left(x^2-2xy+y^2\right)\)
\(=3^2-\left(x-y\right)^2\)
\(=\left(3-x+y\right)\left(3+x-y\right)\)
28 tháng 7 2022
1: \(=a\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(a-4\right)\)
2: \(=x\left(x+b\right)+a\left(x+b\right)=\left(x+b\right)\left(x+q\right)\)
3: \(=a\left(x+1\right)-b\left(x+1\right)+c\left(x+1\right)\)
\(=\left(x+1\right)\left(a-b+c\right)\)
6: \(=\left(x-y\right)^2-4=\left(x-y-2\right)\left(x-y+2\right)\)
16 tháng 8 2020
a) Ta có: \(\left(3x-1\right)^2-16\)
\(=\left(3x-1-4\right)\left(3x-1+4\right)\)
\(=\left(3x-5\right)\left(3x+3\right)\)
\(=3\left(x+1\right)\left(3x-5\right)\)
b) Ta có: \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)
\(=\left(-2x-4\right)\left(12x-4\right)\)
\(=-2\left(x+2\right)\cdot4\cdot\left(3x-1\right)\)
\(=-8\left(x+2\right)\left(3x-1\right)\)
c) Ta có: \(\left(2x+5\right)^2-\left(x-9\right)^2\)
\(=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\)
\(=\left(x+14\right)\left(3x-4\right)\)
d) Ta có: \(\left(3x+1\right)^2-4\left(x-2\right)^2\)
\(=\left(3x+1\right)^2-\left(2x-4\right)^2\)
\(=\left(3x+1-2x+4\right)\left(3x+1+2x-4\right)\)
\(=\left(x+5\right)\left(5x-3\right)\)
e) Ta có: \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)
\(=\left(6x+9\right)^2-\left(2x+2\right)^2\)
\(=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)\)
\(=\left(4x+7\right)\left(8x+11\right)\)
f) Ta có: \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\)
\(=-\left(b^2-2bc+c^2-a^2\right)\left[\left(b^2+2bc+c^2\right)-a^2\right]\)
\(=-\left[\left(b-c\right)^2-a^2\right]\cdot\left[\left(b+c\right)^2-a^2\right]\)
\(=-\left(b-c-a\right)\left(b-c+a\right)\left(b+c-a\right)\left(b+c+a\right)\)
g) Ta có: \(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(=\left(ax+by-ay-bx\right)\left(ax+by+ay+bx\right)\)
\(=\left[a\left(x-y\right)+b\left(y-x\right)\right]\left[a\left(x+y\right)+b\left(x+y\right)\right]\)
\(=\left[a\left(x-y\right)-b\left(x-y\right)\right]\left(x+y\right)\left(a+b\right)\)
\(=\left(x-y\right)\left(a-b\right)\left(x+y\right)\left(a+b\right)\)
h) Ta có: \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left(2ab+4\right)^2\)
\(=\left(a^2+b^2-5+2ab+4\right)\left(a^2+b^2-5-2ab-4\right)\)
\(=\left[\left(a^2+2ab+b^2\right)-1\right]\left[\left(a^2-2ab+b^2\right)-9\right]\)
\(=\left(a+b-1\right)\left(a+b+1\right)\left(a-b-3\right)\left(a-b+3\right)\)
i) Ta có: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)
\(=\left(-6x-18\right)\left(8x^2-18\right)\)
\(=-6\left(x+3\right)\cdot2\left(x^2-9\right)\)
\(=-12\left(x+3\right)^2\cdot\left(x-3\right)\)
k) Ta có: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)
\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)
\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)
\(=\left(-x-3y-5\right)\left(7x+9y-1\right)\)
l) Ta có: \(-4x^2+12xy-9y^2+25\)
\(=-\left(4x^2-12xy+9y^2-25\right)\)
\(=-\left[\left(2x-3y\right)^2-5^2\right]\)
\(=-\left(2x-3y-5\right)\left(2x-3y+5\right)\)
m) Ta có: \(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x-y\right)^2-\left(4m^2-4mn+n^2\right)\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)
21 tháng 8 2017
a)\(\left(3x-1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\)
\(=\left(3x-17\right)\left(3x+15\right)\)
c)\(\left(2x+5\right)^2-\left(x-9\right)^2=\left(2x+5+x-9\right)\left(2x+5-x+9\right)\)
\(=\left(x-4\right)\left(x+14\right)\)
Aps dungj t/c a2 - b2 = ( a-b)(a+b)
10 tháng 10 2016
a) \(ax+ay-3x-3y=a\left(x+y\right)-3\left(x+y\right)=\left(a-3\right)\left(x+y\right)\)
b) \(x^3-3x^2+3x-9=x^2\left(x-3\right)+3\left(x-3\right)=\left(x-3\right)\left(x^2+3\right)\)
c) xem lại đề
d) \(9-x^2-2xy-y^2=9-\left(x+y\right)^2=\left(3-x-y\right)\left(3+x+y\right)\)
\(\text{a) }ax-bx+ab-x^2\\ \\=\left(ax+ab\right)-\left(x^2+bx\right)\\ \\=a\left(x+b\right)-x\left(x+b\right)\\ \\=\left(a-x\right)\left(x+b\right)\\ \)
\(\text{b) }x^2-y^2+4x+4\\ \\ =\left(x^2+4x+4\right)-y^2\\ \\ =\left(x+2\right)^2-y^2\\ \\ =\left(x+2+y\right)\left(x+2-y\right)\\ \)
\(\text{c) }ax+ay-3x-3y\\ \\=\left(ax+ay\right)-\left(3x+3y\right)\\ \\ =a\left(x+y\right)-3\left(x+y\right)\\ \\=\left(a-3\right)\left(x+y\right)\\ \)
\(\text{d) }x^3+x^2+x+1\\ \\=\left(x^3+x^2\right)+\left(x+1\right)\\ \\=x^2\left(x+1\right)+\left(x+1\right)\\ \\=\left(x^2+1\right)\left(x+1\right)\\ \)
\(\text{e) }x^3-3x^2+3x-9\\ \\=\left(x^3-3x^2\right)+\left(3x-9\right)\\ \\ =x^2\left(x-3\right)+3\left(x-3\right)\\ \\=\left(x^2+3\right)\left(x-3\right)\\ \)
\(\text{f) }x^2+ab+ax+bx\\ \\=\left(x^2+ax\right)+\left(bx+ab\right)\\ \\ =x\left(x+a\right)+b\left(x+a\right)\\ \\=\left(x+b\right)\left(x+a\right)\\ \)
\(\text{g) }xy+1+x+y\\ \\=\left(xy+x\right)+\left(y+1\right)\\ \\=x\left(y+1\right)+\left(y+1\right)\\ \\=\left(x+1\right)\left(y+1\right)\)
\(\text{h) }9-x^2-2xy-y^2\\ \\=9-\left(x^2+2xy+y^2\right)\\ \\=3^2-\left(x+y\right)^2\\ \\=\left(3-x-y\right)\left(3+x+y\right)\\ \)
\(\text{i) }x^2-2xy+y^2-1\\ \\=\left(x^2-2xy+y^2\right)-1\\ \\=\left(x-y\right)^2-1^2\\ \\=\left(x-y-1\right)\left(x-y+1\right)\\ \)
d) x3 + x2 + x + 1
= x2(x + 1) + (x + 1)
= (x + 1)(x2 + 1)
e) x3 - 3x2 + 3x - 9
= x2(x - 3) + 3(x - 3)
= (x - 3)(x2 + 3)
f) x2 + ab + ax + bx
= x2 + bx + ab + ax
= x(x + b) + a(b + x)
= (b + x)(x + a)
g) xy + 1 + x + y
= xy + x + y + 1
= x(y + 1) + (y + 1)
= (y + 1)(x + 1)
h) 9 - x2 - 2xy - y2
= 9 - (x2 + 2xy + y2)
= 32 - (x + y)2
= (3 - x - y)(3 + x + y)
i) x2 - 2xy + y2 - 1
= (x - y)2 - 1
= (x - y - 1)(x - y + 1)