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1) a) \(x^3-2x^2y+xy^2-25x=x\left(x^2-2xy+y^2-25\right)\)
\(=x\left[\left(x-y\right)^2-5^2\right]=x\left(x-y-5\right)\left(x-y+5\right)\)
b)\(x^2-y^2-2x-2y=\left(x^2-2x+1\right)-\left(y^2+2y+1\right)=\left(x-1\right)^2-\left(y+1\right)^2\)
\(=\left(x-1-y-1\right)\left(x-y+y+1\right)=\left(x-y-2\right)\left(x+1\right)\)
\(b,2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x+1+y\right)\left(x+1-y\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a)
\(=x^2\left(2x+3\right)+\left(2x+3\right)\)
\(=\left(x^2+1\right)\left(2x+3\right)\)
b)
\(=a\left(a-b\right)+a-b\)
\(=\left(a+1\right)\left(a-b\right)\)
c)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left(x+1-y\right)\left(x+1+y\right)\)
d)
\(=x^3\left(x-2\right)+10x\left(x-2\right)\)
\(=x\left(x^2+10\right)\left(x-2\right)\)
e)
\(=x\left(x^2+2x+1\right)\)
\(=x\left(x+1\right)^2\)
f)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right)\left(x+y\right)\)
a,2x3+3x2+2x+3
=(2x3+2x)+(3x2+3)
=2x(x2+1)+3(x2+1)
=(x2+1)(2x+3)
b,a2-ab+a-b
=(a2-ab)+(a-b)
=a(a-b)+(a-b)
=(a-b)(a+1)
c,2x2+4x+2-2y2
=2(x2+2x+1-y2)
=2[(x2+2x+1)-y2 ]
=2[(x+1)2-y2 ]
=2(x+1-y)(x+1+y)
d,x4-2x3+10x2-20x
=(x4-2x3)+(10x2-20x)
=x3(x-2)+10x(x-2)
=(x-2)(x3+10x)
=(x-2)[x(x2+10)]
e,x3+2x2+x
=x(x2+2x+1)
=x(x+1)2
f,xy+y2-x-y
=(xy+y2)-(x-y)
=y(x+y)-(x+y)
=(x+y)(y-1)
b. x4 - x2 - 2x - 1
=x4-(x2+2x+1)
=x4-(x+1)2
=(x2-x-1)(x2+x+1)
d. ( x2 + 3x + 1 ) ( x2 + 3x - 3 ) - 5
Đặt x2+3x=y
=> (y+1)(y-3)-5=y2-2y-8=(y-1)2-9
=(y-4)(y+2)
=(x2+3x-4)(x2+3x+2)=(x-1)(x+4)(x+1)(x+2)
a)
\(12xy-4x^2y+8xy^2\\ =4xy\cdot\left(3-x+2y\right)\)
b)
\(4x\cdot\left(x-2y\right)-8y\cdot\left(x-2y\right)\\ =4\cdot\left(x-2y\right)\cdot\left(x-2y\right)\\ =4\cdot\left(x-2y\right)^2\)
c)
\(25x^2\cdot\left(y-1\right)-5x^3\cdot\left(1-y\right)\\ =-25x^2\cdot\left(1-y\right)-5x^3\cdot\left(1-y\right)\\ =\left(1-y\right)\cdot\left(-25x^2-5x^3\right)\\ =5x^2\left(1-y\right)\cdot\left(-5-x\right)\)
d)
\(3x\cdot\left(a-x\right)+4a\cdot\left(a-x\right)\\ =\left(a-x\right)\cdot\left(3x+4a\right)\)
e)
\(x^3-3x^2+2\\ =x^3-x^2-2x^2+2\\ =x^2\cdot\left(x-1\right)-2\left(x^2-1\right)\\ =x^2\cdot\left(x-1\right)-2\cdot\left(x-1\right)\cdot\left(x+1\right)\\ =\left(x-1\right)\left[x^2-2\cdot\left(x+1\right)\right]\\ =\left(x-1\right)\cdot-\left(x^2+2x+1\right)\\ =\left(x-1\right)\cdot-\left(x+1\right)^2\)
Bài2: phân tích đa thức thành nhân tử
\(a,x^2-y^2-2x+2y\)
\(=\left(x-y\right)\left(y+x-2\right)\)
\(b,x^3-5x^2+x-5\)
\(=x^2\left(x-5\right)+\left(x-5\right)\)
\(=\left(x+x-5\right)\left(x-x-5\right)\)
\(c,x^2-2xy+y^2-9\)
\(=\left(x^2-y^2\right)-3^2\)
\(=\left(x-y+3\right)\left(x-y-3\right)\)
chúc bạn học tốt !
a) A = (3x - 5)(2x + 11) - (2x + 3)(3x + 7)
A = 6x^2 + 33x - 10x - 55 - 6x^2 - 23x - 21
A = -76
b) B = 4x(3x - 2) - 3x(4x + 1)
B = 12x^2 - 8x - 12x^2 - 3x
B = -11x
c) C = (x + 3)(x - 2) - (x - 1)^2
C = x^2 + x - 6 - x^2 + 2x - 1
C = 3x - 7
Bài làm
a) 4x - 8y
<=> 4( x - 2y )
b) 12x( x - 2y ) - 8y( x - 2y )
<=> ( 12x - 8y )( x - 2y )
<=> 4( 3x - 2y )( x - 2y )
c) 2x + 2y - x2 - xy
= 2( x + y ) - x( x + y )
= ( x + y )( 2 - x )
d) x2 - 4y2
<=> ( x - 2y )( x + 2y )
e) x3 + x2y - 4x - 4y
<=> x2( x + y ) - 4( x + y )
<=> ( x - 2 )( x + 2 )( x + y )
g) 3x2 - 6xy + 3y2 - 12x3
<=>3( x2 - 3xy + y2 - 4x3 )
# Học tốt #
a)4(x-2y)
b)(x-2y)(12x-8y)
=4(x-2y)(3x-2y)
c)2(x+y)-x(x+y)
=(2-x)(x+y)
d)(x-2y)(x+2y)
e)x2(x+y)-4(x+y)
=(x+y)(x2-4)
=(x+y)(x-2)(x+2)
g)3(x2-2xy+y2-4z3)
=3[(x-y)2-4z3]
????????????phải là 4z2chứ nhỉ.....
\(a,=x\left(y^2-25\right)=x\left(y-5\right)\left(y+5\right)\\ b,=x\left(x-y\right)+2\left(x-y\right)=\left(x+2\right)\left(x-y\right)\\ c,=x^2\left(x-3\right)-4\left(x-3\right)\\ =\left(x-2\right)\left(x+2\right)\left(x-3\right)\)