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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 - y2 + x2 - y = (x2 - y2) - (x + y)
= (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
b, x( x + y ) - 5x - 5y = x(x + y) - 5(x + y)
= (x - 5)(x + y)
c, x2 - 5x + 5y - y2 = (x - y)(x + y) - 5(x - y)
= (x - y)(x + y - 5)
d, 5x3 - 5x2y - 10x2 + 10xy = 5x2(x - y) - 10x(x - y)
= 5x(x - y)(x - 2)
e, 27x3 - 8y3 = (3x - 2y)(9x2 + 6xy + 4y2)
f, x2 - y2 - x - y = (x - y)(x + y) - (x + y)
= (x + y)(x - y - 1)
g, x2 - y2 - 2xy + y2 = (x2 - 2xy + y2) - y2
= (x - y)2 - y2
= (x - y - y)(x - y + y) = x(x - 2y)
h, x2 - y2 + 4 - 4x = (x2 - 4x + 4) - y2
= (x - 2)2 - y2
= (x - y - 2)(x + y - 2)
i, x3 + 3x2 + 3x + 1 - 27z3 = (x + 1)3 - 27z3
= (x+1-3z)(x2+2x+1+3xz+3z+9z2)
k, 4x2 + 4x - 9y2 + 1 = (2x + 1)2 - 9y2
= (2x - 3y + 1)(2x + 3y + 1)
m, x2 - 3x + xy - 3y = x(x - 3) + y(x - 3)
= (x - 3)(x + y)
a) \(-x-y^2+x^2-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right).1\)
\(=\left(x+y\right)\left(x-y-1\right)\)
b) \(x\left(x+y\right)-5x-5y\)
\(=x\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x+y\right)\left(x-5\right)\)
c) \(x^2-5x+5y-y^2\)
\(=\left(x^2-y^2\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
d) \(5x^3-5x^2y-10x^2+10xy\)
\(=5x\left(x^2-xy-2x+2y\right)\)
\(=5x\left[x\left(x-y\right)-2\left(x-y\right)\right]\)
\(=5x\left(x-y\right)\left(x-2\right)\)
e) \(27x^3-8y^3\)
\(=\left(3x\right)^3-\left(2y\right)^3\)
\(=\left(3x-2y\right)\left[\left(3x\right)^2+3x2y+\left(2y\right)^2\right]\)
\(=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)
f) \(x^2-y^2-x-y\)
\(=\left(x^2-y^2\right)-\left(x+y\right)\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
g) \(x^2-y^2-2xy+y^2\)
\(=\left(x^2-2xy+y^2\right)-y^2\)
\(=\left(x-y\right)^2-y^2\)
\(=\left(x-y-y\right)\left(x-y+y\right)\)
\(=\left(x-y^2\right)x\)
h) \(x^2-y^2+4-4x\)
\(=\left(x^2-4x+4\right)-y^2\)
\(=\left(x^2-2.2x+2^2\right)-y^2\)
\(=\left(x-2\right)^2-y^2\)
\(=\left(x-2-y\right)\left(x-2+y\right)\)
i) \(x^6-y^6\)
\(=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=\left[\left(x-y\right)\left(x^2+xy+y^2\right)\right]\left[\left(x+y\right)\left(x^2-xy+y^2\right)\right]\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
mình đánh máy vội nên sai mn đừng trả lời câu này nha !!!!
Bài 4:
a: \(\Leftrightarrow x^3-3x^2+3x-1-x^3-27+3x^2-12=2\)
\(\Leftrightarrow3x-40=2\)
=>3x=42
hay x=14
b: \(\Leftrightarrow x^3+8-x^3-2x=0\)
=>-2x+8=0
=>-2x=-8
hay x=4
c: \(x\left(x-2\right)+\left(x-2\right)=0\)
=>(x-2)(x+1)=0
=>x=2 hoặc x=-1
d: \(5x\left(x-3\right)-x+3=0\)
=>5x(x-3)-(x-3)=0
=>(x-3)(5x-1)=0
=>x=3 hoặc x=1/5
e: \(3x\left(x-5\right)-\left(x-1\right)\left(3x+2\right)=30\)
\(\Leftrightarrow3x^2-15x-3x^2-2x+3x+2=30\)
=>-14x=28
hay x=-2
f: \(\Leftrightarrow\left(x+2\right)\left(x+30-x-5\right)=0\)
=>x+2=0
hay x=-2
\(3x^2\left(x-1\right)+5x\left(1-x\right)^2\\ =-3x^2\left(1-x\right)+5x\left(1-x\right)\left(1-x\right)\\ =\left(1-x\right)\left(-3x^2+5x-5x^2\right)\\ =x\left(1-x\right)\left(-3x+5-5x\right)\\ =x\left(1-x\right)\left(5-8x\right)\)
\(3\left(x-y\right)^2+9y\left(y-x\right)^2\\ =3\left(x-y\right)\left(x-y\right)+9y\left(y-x\right)\left(y-x\right)\\ =-3\left(x-y\right)\left(y-x\right)+9y\left(y-x\right)\left(y-x\right)\\ =\left(y-x\right)\left(-3x+3y+9y^2-9xy\right)\\ =\left(y-x\right)\left[-3\left(x-y\right)+9y\left(y-x\right)\right]\\ =\left(y-x\right)\left[-3\left(x-y\right)-9y\left(x-y\right)\right]\\ =\left(y-x\right)\left(-3-9y\right)\left(x-y\right)\\ =-3\left(y-x\right)\left(1+3y\right)\left(x-y\right)\)
\(3\left(x-y\right)^2+9y\left(y-x\right)\\ =3\left(x-y\right)\left(x-y\right)-9y\left(x-y\right)\\ =\left(x-y\right)\left(3x-3y-9y\right)\\ =\left(x-y\right)\left(3x-12y\right)\\ =3\left(x-y\right)\left(x-4y\right)\)