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A = x2(x - 1) + 6(1 - x)
A = x3 - x2 + 6 - 6x
A = (x3 - 6x) - (x2 - 6)
A = x.(x2 - 6) - (x2 - 6)
A = (x - 1)(x2 - 6)
C = x2 + 2xy + y2 - yz - xz
C = (x + y)2 - z.(x + y)
C = (x + y - z).(x + y)
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)\(81x^2-6yz-9y^2-z^2\)
\(=81x^2-\left(z-3y\right)^2\)
\(=\left(9x-z+3y\right)\left(9x+z-3y\right)\)
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.5X2+3(X+Y)2-5Y2
= 5.(x2 - y2) + 3(x+y)2
=5.( x-y).(x+y) +3(x+y)2
= ( x+y).[(5.( x-y) + 3(x+y)]
=( x+y).( 5x-5y +3x + 3y)
=( x+y).( 8x - 2y)
=( x+y).2(4x - y)
C.81x2 - 6yz - 9y2 - z2
=( 9x)2 - (z2 + 6yz+ 9y2)
=( 9x)2 -( z +3y)2
=(9x - z -3y).(9x + z+3y)
D.x2y-x3-9y+9x
=9.(x - y) + x2(y - x)
= 9.(x-y) - x2(x-y)
=(x+y).[32- x2]
=(x+y).(3-x).(x+2)
E.x3+9x2-4x-36
=(x3-4x) + (-36 +9x2)
=x.(x2-4) + 9.(x2-4)
=(x2-4).(x+9)
H.2x3+x2-8x-4
= x2.(2x+1)-4.(2x +1)
=(2x +1).(x2 -4)
= (2x +1).(x-2).(x+2)
Cậu xem trước nhé
phân tích đa thức thành nhân tử
a,a2+2ab+b2-ac-bc
= ( a2 + 2ab + b2 ) - (ac+bc)
= (a+b)2 - c(a+b)
=(a+b)(a+b-c)
b,x2+8x+15
= x2 + 3x+5x+ 15
= (x2 + 3x)+(5x+ 15)
= x(x+3) + 5(x+3)
= (x+3)(x+5)
c,x2y-x3-9y+9x
= (x2y -x3)-(9y-9x)
= x2(y-x)-9(y-x)
= (y-x)(x2-9)
= (y-x)(x-3)(x+3)
d,81x2+4
= (9x)2+22
=(9x)2+2.9x.2+22-36x
=(9x+2)2-36x
=(9x+2-6√x)(9x+2+6√x)
câu a) mk nghỉ đề dầy mới đúng : \(a^2+2ab+b^2-ac-bc\)
\(=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b-c\right)\left(a+b\right)\)
b) \(x^2+8x+15=x^2+3x+5x+15=x\left(x+3\right)+5\left(x+3\right)\)
\(=\left(x+5\right)\left(x+3\right)\)
c) \(x^2y-x^3-9y+9x=x^2\left(y-x\right)-9\left(y-x\right)\)
\(=\left(x^2-9\right)\left(y-x\right)=\left(x-3\right)\left(x+3\right)\left(y-x\right)\)
d) câu này mk nghỉ là đề như thế này mới đúng : \(81x^2-4\)
\(=\left(9x\right)^2-2^2=\left(9x-2\right)\left(9x+2\right)\)
\(b,9x^2+90x+225-\left(x-y\right)^2\)
\(=\left(3x+15\right)^2-\left(x-y\right)^2\)
\(=\left(3x+15-x+y\right)\left(3x+15+x-y\right)\)
\(=\left(2x+y+15\right)\left(4x-y+15\right)\)
\(81x^2-6yz-9y^2-z^2=81x^2-\left(6yz+9y^2+z^2\right)\)
\(=81x^2-\left(9y^2+6xy+z^2\right)=81x^2-\left(3y+z\right)^2\)
\(=\left(9x-3y-z\right)\left(9x+3y+z\right)\)
\(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
\(49\left(y-4\right)^2-9y^2-36y-36\)
\(=49\left(y-4\right)^2-\left(9y^2+36y+36\right)\)
\(=49\left(y-4\right)^2-\left(3y+6\right)^2\)
\(=[7\left(y-4\right)]^2-\left(3y+6\right)^2\)
\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)
\(=\left(7y-28+3y+6\right)\left(7y-28-3y-6\right)\)
\(=\left(10y-22\right)\left(4y-34\right)\)
a) = x2 (y - x) - 9( y - x) = ( y - x ) ( x2 - 9) = ( y -x) ( x - 3 ) ( x + 3)
b) = x2 ( x - 1 ) - 16 ( x - 1 ) = ( x - 1 ) ( x2 - 16 ) = ( x - 1 ) ( x - 4 ) ( x + 4 )
c) = (9x)2 - ( 9y2 + 6yz + z2 ) = (9x)2 - ( 3y + z)2 = (9x - 3y - z ) ( 9x + 3y + z)
d) = z( x - y) - ( x2 -2xy + y2 ) = z(x - y) - (x - y)2 = (x - y) (z - 1)
e) = (x + 3) (x + 5)
f) = (x - 4) ( x + 3)
g) = (9x)2 + 2.9x.2 + 22 - 36x = (9x + 2)2 - (\(6\sqrt{x}\))2 = \(\left(9x+2+6\sqrt{x}\right)\). \(\left(9x+2-6\sqrt{x}\right)\)
a) x2y - x3 - 9y + 9x = x2(y - x) - 9(y - x) = (y - x)(x2 - 9) = (y - x)(x + 3)(x - 3).
b) x2(x - 1) + 16(1 - x) = (x - 1)(x2 - 16) = (x - 1)(x - 4)(x + 4).
c) 81x2 - 6yz - 9y2 - z2 = (9x)2 - ((3y)2 + 2.3yz + z2) = (9x)2 - (3y + z)2 = (9x + 3y +z)(9x - 3y - z).
d) xz - yz - x2 + 2xy - y2 = z(x - y) - (x - y)2 = (x - y)(z - x + y).
e) x2 + 8x + 15 = (x2 + 3x) + (5x + 15) = x(x + 3) + 5(x + 3) = (x + 3)(x + 5).
f) x2 - x - 12 = (x2 - 4x) + (3x - 12) = x(x - 4) + 3(x - 4) = (x - 4)(x + 3).
g) (Đề sai) 81x4 + 4 = (81x4 + 36x2 + 4) - 36x2 = (9x2 + 2)2 - 36x2 = (9x2 + 2 + 6x)(9x2 + 2 - 6x).