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a)\(81x^2-6yz-9y^2-z^2\)
\(=81x^2-\left(z-3y\right)^2\)
\(=\left(9x-z+3y\right)\left(9x+z-3y\right)\)
b)\(x^2y-x^3-9y+9x\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
c)\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4z^2\right)\)
\(=3\left[\left(a-b\right)^2-4z^2\right]\)
\(=3\left(a-b-2z\right)\left(a-b+2z\right)\)
a)\(81x^2-6yz-9y^2-z^2=\left(9x\right)^2-\left(9y^2+6yz+z^2\right)=\left(9x\right)^2-\left(3y+z\right)^2=\left(9x-3y-z\right)\left(9x+3y+z\right)\)b)\(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)=\left(x^2-9\right)\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
c)\(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]=3\left(a-b-2c\right)\left(a-b+2c\right)\)
a ) \(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=4\left(a-b-2c\right)\left(a-b+2c\right)\)
b ) \(x^2-25+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
c )
\(x^2y-x^3-9y+9x\)
\(=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(y-x\right)\left(x^2-9\right)\)
\(=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
d )\(x^2\left(x-1\right)+16\left(1-x\right)\)
\(=x^2\left(x-1\right)-16\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-16\right)\)
\(=\left(x-1\right)\left(x-4\right)\left(x+4\right)\)
\(a,2x^2-2xt-5x+5y\)
\(=\left(2x^2-5x\right)-\left(2xy-5y\right)\)
\(=x\left(2x-5\right)-y\left(2x-5\right)\)
\(=\left(2x-5\right)\left(x-y\right)\)
\(b,8x^2+4xy-2ax-ay\)
\(=\left(8x^2-2ax\right)+\left(4xy-ay\right)\)
\(=2x\left(4x-a\right)+y\left(4x-a\right)\)
\(=\left(4x-a\right)\left(2x+y\right)\)
\(c,x^3-4x^2+4x\)
\(=x^3-2x^2-2x^2+4x\)
\(=\left(x^3-2x^2\right)-\left(2x^2-4x\right)\)
\(=x^2\left(x-2\right)-2x\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2-2x\right)=x\left(x-2\right)\left(x-2\right)\)
\(=x\left(x-2\right)^2\)
\(d,2xy-x^2-y^2+16\)
\(=-\left(x^2-2xy+y^2-16\right)\)
\(=-\left[\left(x-y\right)^2-4^2\right]\)
\(=-\left(x-y-4\right)\left(x-y+4\right)\)
\(e,x^2-y^2-2yz-z^2\)
\(=x^2-\left(y^2+2yz+z^2\right)\)
\(=x^2-\left(y+z\right)^2=\left(x-y-z\right)\left(x+y+z\right)\)
\(x^3-x^2-5x+125\)
\(=\left(x+5\right)\left(x^2-5x+25\right)-x\left(x+5\right)\)
\(=\left(x+5\right)\left(x^2-5x+25-x\right)\)
\(=\left(x+5\right)\left(x^2-6x+25\right)\)
\(x^6-x^4-9x^3+9x^2\)
\(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)
\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)
\(=x^2\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)
\(=x^2\left(x-1\right)\left(x^3+x^2-9\right)\)
\(x^4-4x^3+8x^2-16x+16\)
\(=\left(x^2+4\right)^2-4x\left(x^2+4\right)\)
\(=\left(x^2+4\right)\left(x^2+4-4x\right)\)
\(=\left(x^2+4\right)\left(x-2\right)^2\)
\(3a^2-6ab+3b^2-12c^2\)
\(=3\left(a^2-2ab+b^2-4c^2\right)\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]\)
\(=3\left(a-b+2c\right)\left(a-b-2c\right)\)
câu 1
a, 5x - x 2 + 2xy - 5y
= 5x - x 2 + xy + xy - 5y
= ( 5x - 5y ) - ( x2 - xy ) + xy
= 5 ( x-y ) - x(x-y ) + xy
= (5-x) ( x-y) + xy
mik làm dc mỗi câu a !
a. 6x3y2 ( 2-x) + 9x2y2 (x-2)
= -6x3y2 (x-2) + 9x2y2 ( x-2)
= (x-2) 3x2y2 ( -2x + 3)
b. x2 - 4x + 4y - y2
= x2 - y2 - (4x - 4y )
= (x-y)(x+y) - 4( x-y)
= (x-y)(x+y-4)
c. 81x2 + 6yz -9y2-z2
= 81x2 - (9y2 - 6yz + z2 )
= (9x)2 - ( 3y - z )2
= (9x + 3y -z)(9x - 3y + z )
\(a,=6x^3y^2\left(2-x\right)-9x^2y^2\left(2-x\right)\)
\(=\left(2-x\right)\left(6x^3y^2-9x^2y^2\right)=\left(2-x\right)3x^2y^2\left(2x-3\right)\)
\(f,=\left(x-3-x-2\right)\left(x-3+x+2\right)\)
\(=-5\left(2x-1\right)\)
\(g,=\left(x-3\right)\left(x+3\right)+2\left(x+3\right)\)
\(=\left(x+3\right)\left(x-3+2\right)\)
\(=\left(x+3\right)\left(x-1\right)\)
a. x4+2= (x4+\(2\sqrt{2}x^2+2\)) - \(2\sqrt{2}x^2^{ }\) =
\(\left(x^2+\sqrt{2}\right)^2-2\sqrt{2}x^2=\left(x^2-\sqrt{2\sqrt{2}}x+\sqrt{2}\right)\left(x^2+2\sqrt{2}x+\sqrt{2}\right)\)b. 81x2-(9y2+6yz+z2)=81x2 - (3y+z)2=(9x-3y-z)(9x+3y+z)
Bài làm:
a) x2 - y2 - 2x + 2y = (x - y)(x + y) - (2x - 2y)
= (x - y)(x + y) - 2(x - y)
= [(x + y) - 2].(x - y)
= (x + y - 2)(x - y)
c)3a2 - 6ab + 3b2 - 12c2 = (3a2 - 6ab + 3b2) - 12c2
= 3(a2 - 2ab + b2) - 12c2
= 3[(a - b)2] - 12c2
= 3[(a - b)2 - 4c2]
= 3[(a - b)2 - (2c)2]
= 3[(a - b - c) - (a - b + c)]
= 3(a - b - c - a + b - c)
= 3(-2c)
= -6c
d)x2 - 5 + y2 + 2xy = (x2 + 2xy + y2) - 5
= (x + y)2 - 5
= (x + y)2 -(\(\sqrt{5}\))2
= (x + y - \(\sqrt{5}\)) - (x + y + \(\sqrt{5}\))
= x + y - \(\sqrt{5}\) - x - y -\(\sqrt{5}\)
= -2\(\sqrt{5}\)
e) a2 + 2ab + b2 - ac - bc = (a2 + 2ab + b2) - (ac + bc)
= (a + b)2 - c(a + b)
= [(a + b) - c].(a + b)
= (a + b - c)(a + b)
Còn câu b) và câu f) Vàng sẽ nghĩ sau :v
Tiếp câu f luôn !
\(x^2-2x-4y^2-4y\)
\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\(a,36x^2-\left(3x-2\right)^2=\left(6x-3x+2\right)\left(6x+3x-2\right)\)
\(=\left(3x+2\right)\left(9x-2\right)\)
phần b,c,d lm tg tự
\(e,16x^2-24xy+9y^2=\left(4x-3y\right)^2\)
a) (x2-y2)+(2x+2y)
= (x-y)(x+y)+2(x+y)
= (x+y)(x-y+2)
b) (3a2-6ab+3b2)-12c2
= 3(a2-2ab+b2)-12c2
= 3(a-b)2-3.(2c)2
= 3[(a-b)2-(2c)2]
= 3(a-b-2c)(a-b+2c)
c) (x2+2xy+y2)-25
= (x+y)2-25=(x+y-5)(x+y+5)
d) 81x2-(z2+6yz+9y2)=(9x)2-(z+3y)2=(9x-z-3y)(9x+z+3y)
Bài dễ muốn chết mà giải không được. Chắc do đến Tết lười nè! Nói chơi thôi chứ ai mà không như vậy.
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) \(3a^2-6ab+3b^2-12c^2=3\left(a^2-2ab+b^2-4c^2\right)=3\left[\left(a^2-2ab+b^2\right)-4c^2\right]\)
\(=3\left[\left(a-b\right)^2-\left(2c\right)^2\right]=3\left(a-b+2c\right)\left(a-b-2c\right)\).
c) \(x^2-25+y^2+2xy=\left(x^2+2xy+y^2\right)-25=\left(x+y\right)^2-5^2\)
\(=\left(x+y+5\right)\left(x+y-5\right)\).
d) \(81x^2-6yz-9y^2-z^2=81x^2-\left(9y^2+6yz+z^2\right)\)
\(=81x^2-\left[\left(3y\right)^2+2.3y.z+z^2\right]=\left(9x\right)^2-\left(3y+z\right)^2=\left(9x+3y+z\right)\left(9x-3y-z\right)\).
Mình không biết bạn ở trình độ nào nên mình làm chi tiết như vậy. Khi giải, bạn có thể lược bỏ một số bước nếu bạn thấy không cần thiết.