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a) Ta có : a2x + a2y - 7x - 7y
= a2(x + y) - (7x + 7y)
= a2(x + y) - 7(x + y)
= (x + y)(a2 - 7)
b) Ta có : x3 + y(1 - 3x2) + x(3x2 - 1) - y3
= x3 - y(3x2 - 1) + x(3x2 - 1) - y3
= x3 - y3 + [x(3x2 - 1) - y(3x2 - 1)]
= x3 - y3 - (3x2 - 1)(x - y)
= (x - y)(x2 + xy + y2) - (3x2 - 1)(x - y)
= (x - y)[(x2 + xy + y2) - (3x2 - 1)]
= (x - y)(x2 + xy + y2 - 3x2 + 1)
= (x - y)(-2x2 + xy + y2 + 1)
bài 2:a. \(5x.\left(y^2-2yz+z^2\right)\)
\(=5x.\left(y-z\right)^2\) .......k bít dc chưa
b.\(\left(x^2y-x\right)+\left(xy^2-y\right)\)
\(=x.\left(xy-1\right)+y.\left(xy-1\right)\)
\(=\left(xy-1\right).\left(x+y\right)\)
Câu a trước đi ạ ^^
a) 7x - 6x2 - 2
= - 6x2 + 7x - 2
= (- 6x2 + 3x) + (4x - 2)
= 3x (- 2x + 1) + 2 (2x-1)
= - 3x ( 2x -1) + 2 (2x - 1)
= ( 2x -1 ) ( - 3x +2 )
a: \(x^4+3x^3+x^2+3x\)
\(=x\left(x^3+3x^2+x+3\right)\)
\(=x\left(x+3\right)\left(x^2+1\right)\)
c: \(x^2-xy-x+y\)
\(=x\left(x-y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x-1\right)\)
\(a,4\left(2-x\right)^2+xy-2y\)
\(=4\left(2-x\right)^2-y\left(2-x\right)\)
\(=4-y\left(2-x\right)^2\left(2-x\right)\)
\(=\left(2-x\right)\left[\left(2-x\right)4-y\right]\)
\(=\left(2-x\right)\left(4x-8+y\right)\)
\(c,x^3+y^3+z^3-3xyz\)
\(=x^3+y^3+z^3+3x^2y-3x^2y+3xy^2-3xy^2-3xyz\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-3x^2y-3xy^2+z^3-3xyz\)
\(=\left(x+y\right)^3-3xy\left(x+1\right)+z^3-3xyz\)
\(=\left[\left(x+y\right)^3+z^3\right]-3xy\left(x+y\right)-3xyz\)
\(=\left[\left(x+y\right)+z\right]\left[\left(x+y\right)^2-\left(x+y\right)z+z^2\right]-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+2xy+y^2-xz-yz+z^2\right)-3xy\left(x+y+z\right)\)
\(=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-xz-yz\right)\)
a) 4(2 - x)2 + xy - 2y = 4(x - 2)2 + y(x - 2) = (4x - 8 + y)(x - 2)
b) 2(x - 1)3 - 5(x - 1)2 - (x - 1) = (x - 1)[2(x - 1)2 - 5(x - 1) - 1]
= (x - 1)(2x2 - 4x + 2 - 5x + 5 - 1) = (x - 1)(2x2 - 9x + 6)
c) x3 + y3 + z3 - 3xyz = (x + y)(x2 - xy + y2) + z3 - 3xyz
= (x + y)3 + z3 - 3xy(x + y) - 3xyz = (x + y + z)(x2 + 2xy + y2 - xz - yz + z2) - 3xy(x + y + z)
= (x + y + z)(x2 + y2 + z2 - xz - yz + 2xy - 3xy) = (x + y + z)(x2 + y2 + z2 - xy - yz - xz)
