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Câu a nhé: 2x . x^2 - 2x . 7x - 2x . 3 = 2x^3 - 14x^2 - 6x
a) \(2x^2-2y^2\)
\(=2\left(x^2-y^2\right)\)
\(=2\left(x-y\right)\left(x+y\right)\)
b) \(x^2-4x+4\)
\(=x^2-2\cdot x\cdot2+2^2\)
\(=\left(x-2\right)^2\)
c) \(x^2+2x+1-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x-y+1\right)\left(x+y+1\right)\)
d) \(x^2-4x\)
\(=x\left(x-4\right)\)
e) \(x^2+10x+25\)
\(=x^2+2\cdot x\cdot5+5^2\)
\(=\left(x+5\right)^2\)
g) \(x^2-2xy+y^2-9\)
\(=\left(x-y\right)^2-3^2\)
\(=\left(x-y-3\right)\left(x-y+3\right)\)
h) \(2x^2-2\)
\(=2\left(x^2-1\right)\)
\(=2\left(x-1\right)\left(x+1\right)\)
i) \(5x^2-5xy+9x-9y\)
\(=5x\left(x-y\right)+9\left(x-y\right)\)
\(=\left(x-y\right)\left(5x+9\right)\)
k) \(y^2-4y+4-x^2\)
\(=\left(y-2\right)^2-x^2\)
\(=\left(y-x-2\right)\left(y+x-2\right)\)
l) \(x^2-16\)
\(=x^2-4^2\)
\(=\left(x-4\right)\left(x+4\right)\)
m) \(3x^2-3xy+2x-2y\)
\(=3x\left(x-y\right)+2\left(x-y\right)\)
\(=\left(x-y\right)\left(3x+2\right)\)
o) \(3x^4-6x^3+3x^2\)
\(=3x^2\left(x^2-2x+1\right)\)
\(=3x^2\left(x-1\right)^2\)
a) 2x2 - 2y2
= (2x - 2y)(2x + 2y)
= 4(x - y)(x + y)
b) x2 - 4x + 4
= (x - 2)2
c) x2 + 2x + 1 - y2
= (x + 1)2 - y2
= (x + 1 - y)(x + 1 + y)
d) x2 - 4x
= x(x - 4)
e) x2 +10x + 25
= (x + 5)2
g) x2 - 2xy + y2 - 9
= (x - y)2 - 32
= (x - y - 3)(x - y + 3)
h) 2x2 - 2
= 2(x2 - 1)
= 2(x - 1)(x + 1)
i) 5x2 - 5xy + 9x - 9y
= 5x(x - y) + 9(x- y)
= (5x + 9)(x - y)
k) y2 - 4y + 4 - x2
= (y - 2)2 - x2
= (y - 2 - x)(y - 2 + x)
l) x2 - 16
= x2 - 42
= (x - 4)(x + 4)
m) 3x2 - 3xy + 2x -2y
= 3x(x - y) +2(x-y)
= (3x + 2)(x - y)
o) 3x4 - 6x3 + 3x2
= 3x4 - 3x3 - 3x3 + 3x2
= 3x3(x - 1) - 3x2(x - 1)
= (3x3 - 3x2)(x - 1)
= 3x2(x - 1)(x - 1)
= 3x2.(x - 1)2
\(a. 2x(3x^2-5x+3) = 6x^3-10x^2+6x \)
\(b. -2x(x^2+5x-3) = -2x^3-10x^2+6x\)
c. \(-\dfrac{1}{2}x^2\left(2x^3-4x+3\right)
=-x^5+2x^3-\dfrac{3}{2}x^2\)
\(d.\left(2x-1\right)\left(x^2+5-4\right)=\left(2x-1\right)\left(x^2+1\right)=2x^3+2x-x^2-1\)
e. \(-\left(5x-4\right)\left(2x+3\right)=10x^2+15x-8x-12=-10x^2+7x-12\)
f.\(\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)
g.\(\left(3x-4\right)\left(x+4\right)+\left(5-x\right)\left(2x^2+3x-1\right)=3x^2+12x-4x-16+10x^2+15x-5-2x^3-3x^2+x=-2x^3+10x^2+24x-21\)
e. \(7x\left(x-4\right)-\left(7x+3\right)\left(2x^2-x+4\right)=7x^2-28x-14x^3+7x^2-28x-6x^2+3x+-12=-14x^3+8x^2-53x-12\)
sau bạn đăng tách ra cho mn cùng giúp nhé
a, \(\left(-2x^5+3x^2-4x^3\right):2x^2=-x^3+\frac{3}{2}-2x\)
b, \(\left(x^3-2x^2y+3xy^2\right):\left(-\frac{1}{2}x\right)=-\frac{x^2}{2}+xy-\frac{3y^2}{2}\)
c, \(\left(3x^2y^2+6x^3y^3-12xy^2\right):3xy=xy+2x^2y^2-4y\)
d, \(\left(4x^3-3x^2y+5xy^2\right):\frac{1}{2}x=2x^2-\frac{3xy}{2}+\frac{5y^2}{2}\)
e, \(\left(18x^3y^5-9x^2y^2+6xy^2\right):3xy^2=6x^2y^3-3x+2\)
f, \(\left(x^4+2x^2y^2+y^4\right):\left(x^2+y^2\right)=\left(x^2+y^2\right)^2:\left(x^2+y^2\right)=x^2+y^2\)
a) \(3x^2-3y^2-x-y\)
\(\Leftrightarrow3\left(x^2-y^2\right)-x-y\)
\(\Leftrightarrow3\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(\Leftrightarrow3\left(x-y\right)\)
d) \(3x^2-7x+4\)
\(\Leftrightarrow3x^2-7x+7-3\)
\(\Leftrightarrow\left(3x^2-3\right)-\left(7x-7\right)\)
\(\Leftrightarrow3\left(x^2-1\right)-7\left(x-1\right)\)
\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)-7\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(3\left(x+1\right)-7\right)\)
\(\Leftrightarrow\left(x+1\right)\left(3x-6\right)\)
e) \(-2x^2+3x-1\)
\(\Leftrightarrow\left(-2x^2-1^2\right)+3x\)
\(\Leftrightarrow\left(-2x-1\right)\left(-2x+1\right)+3x\)
f) \(x^2+2xy+y^2-2x-2y\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
k) \(2x^2+5x+3\)
\(\Leftrightarrow2x^2+2x+3x+3\)
\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)\)
\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)\)
l) \(x^2-2x-y^2+1\)
\(\Leftrightarrow\left(x^2-2x+1\right)-y^2\)
\(\Leftrightarrow\left(x-1\right)^2-y^2\)
\(\Leftrightarrow\left(x-1-y\right)\left(x-1+y\right)\)
a) \(3x^2-3y^2-x-y\)
\(\Leftrightarrow3\left(x^2-y^2\right)-x-y\)
\(\Leftrightarrow3\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(\Leftrightarrow3\left(x-y\right)\)
d) \(3x^2-7x+4\)
\(\Leftrightarrow3x^2-7x+7-3\)
\(\Leftrightarrow\left(3x^2-3\right)-\left(7x-7\right)\)
\(\Leftrightarrow3\left(x^2-1\right)-7\left(x-1\right)\)
\(\Leftrightarrow3\left(x-1\right)\left(x+1\right)-7\left(x-1\right)\)
\(\Leftrightarrow\left(x-1\right)\left(3\left(x+1\right)-7\right)\)
\(\Leftrightarrow\left(x+1\right)\left(3x-6\right)\)
e) \(-2x^2+3x-1\)
\(\Leftrightarrow\left(-2x^2-1^2\right)+3x\)
\(\Leftrightarrow\left(-2x-1\right)\left(-2x+1\right)+3x\)
f) \(x^2+2xy+y^2-2x-2y\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
\(\Leftrightarrow\left(x+y\right)^2-2\left(x+y\right)\)
k) \(2x^2+5x+3\)
\(\Leftrightarrow2x^2+2x+3x+3\)
\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)\)
\(\Leftrightarrow\left(2x+3\right)\left(x+1\right)\)
l) \(x^2-2x-y^2+1\)
\(\Leftrightarrow\left(x^2-2x+1\right)-y^2\)
\(\Leftrightarrow\left(x-1\right)^2-y^2\)
\(\Leftrightarrow\left(x-1-y\right)\left(x-1+y\right)\)