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a , \(81x^2y+18xy^2+27x^2y^2\)\(=9xy\left(9x+2y+3xy\right)\)
b. \(4x^3+x^2+x=x\left(4x^2+x+1\right)\)
c. \(x^6+y^6=\left(x^2\right)^3+\left(y^2\right)^3\)\(=\left(x^2+y^2\right)\left(x^4-x^2y^2+y^4\right)\)
d.
e. \(\left(x+y\right)^3-\left(x-3\right)^3\)\(=x^3+3x^2y+3xy^2+y^3-x^3+9x^2-27x-y^3\)
\(=3x^2y+3xy^2+9x^2-27x\)
\(=3x\left(xy+y^2+3x-9\right)\)
h. \(x^2+x+\frac{1}{4}=\)\(4x^2+4x+1=\left(2x+1\right)^2=\left(2x+1\right)\left(2x+1\right)\)
i.
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).
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)
1: \(=\left(x-1\right)\left(3x+7x^2\cdot2\right)=\left(x-1\right)\cdot x\cdot\left(3+14x\right)\)
2: \(=\left(x-y\right)\left(x^2+1\right)\)
3: \(=4x\cdot\left(x-2y\right)-8y\left(x-2y\right)\)
\(=4\left(x-2y\right)\left(x-2y\right)=4\left(x-2y\right)^2\)
5: \(=x^2\left(25-\dfrac{1}{81}y^2\right)=x^2\left(5-\dfrac{1}{9}y\right)\left(5+\dfrac{1}{9}y\right)\)
b. Câu hỏi của gorosuke - Toán lớp 8 - Học toán với OnlineMath
a) 10x(x - y)2 - 5(x - y)3 = [10x - 5(x - y)](x - y)2 = (10x - 5x + y)(x - y)2 = (5x + y)(x - y)2
b) -x2 - 10x - 25 = -(x2 + 10x + 52) = -(x + 5)2
c) 64x6y4 - 81x2y2 = (8x3y2)2 - (9xy)2 = (8x3y2 + 9xy)(8x3y2 - 9xy)
d) x6 - y6 = (x3)2 - (y3)2 = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy + y2)(x + y)(x2 - xy + y2)
e)1/8x3 - 3/4x2y + 3/2xy2 - y3 = (1/2x)3 - 3.(1/2x)2y + 3.1/2xy2 - y3 = (1/2x - y)3
f) (3x + 1)2 - (x - 1)2 = (3x + 1 + x - 1)(3x + 1 - x + 1) = 4x(2x + 2) = 8x(x + 1)
a)\(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(x^3+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)
b)\(x^4-x^3-x^2+1=\left(x^4-x^3\right)-\left(x^2-1\right)=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
c)\(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)
y [x2+x(x-y)+(x2+x+1)+81x(x-1)]
= y (x2+x2-xy+x2+x+1+81x2-81x)
= y (84x2-xy-80x+1)
= 84x2y-xy2-80xy+y