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1 Điền vào chỗ chấm để có hằng đẳng thức thích hợp :
a) x2 - 4y2 = ........(x-2y)(x+2y)......................
b) 1/42 + 2xy + 4y2 =.............(1/4+2y)2..........................
c) 64x3 - 1 =..................(4x-1)(16x2+4x+1)................
d) 25 + 10y + y2 =........(5+y)2....................
b, x2 + 9x - 10
= x2 + 10x - x -10
= ( x2 - x ) +(10x - 10)
=x( x - 1) + 10 ( x - 1)
= ( x - 1)(x + 10 )
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)
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)
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
a ) \(24a^2b-36ab^2-60b^3\)
\(=12b\left(2a^2-3ab-5b^2\right)\)
b ) \(2x^2y-3x+3x^2-2xy\)
\(=\left(2x^2y-2xy\right)+\left(3x^2-3x\right)\)
\(=2xy\left(x-1\right)+3x\left(x-1\right)\)
\(=\left(2xy+3x\right)\left(x-1\right)\)
\(=x\left(2y+3\right)\left(x-1\right)\)
c ) \(x^2-y^2-6x+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2\)
\(=\left(x-3-y\right)\left(x-3+y\right)\)
:D
\(a,2a^2b-36ab^2-60b^3\)
\(=12b\left(2a^2-3ab-5b^2\right)\)
\(=12b\left(2a^2-5ab+2ab-5b^2\right)\)
\(=12b\left[a\left(2a-5b\right)+b\left(2a-5b\right)\right]\)
\(=12b\left(a+b\right)\left(2a-5b\right)\)
\(b,2x^2y-3x+3x^2-2xy\)
\(=\left(2x^2y-2xy\right)+\left(3x^2-3x\right)\)
\(=2xy\left(x-1\right)+3x\left(x-1\right)\)
\(=\left(2xy+3x\right)\left(x-1\right)\)
\(=x\left(2y+3\right)\left(x-1\right)\)
\(c,x^2-y^2-6x+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x^2-2.x.3+3^2\right)-y^2\)
\(=\left(x-3\right)^2-y^2\)
\(=\left(x-3-y\right)\left(x-3+y\right)\)
Chúc bạn hok tốt!!!