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\(b,2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x+1+y\right)\left(x+1-y\right)\)
a) 2x3 + 8x2 - 8x
= 2x(x2 + 4x - 4)
= 2x(x2 + 4x + 4 - 8)
= 2x[(x + 2)2 - 8]
= \(2x\left(x+2-\sqrt{8}\right)\left(x+2+\sqrt{8}\right)\)
b) a2 - b2 + 4a + 4b
= (a - b)(a + b) + 4(a + b)
= (a + b)(a - b + 4)
c) x2 - 2x - 3
= x2 + x - 3x - 3
= x(x + 1) - 3(x + 1)
= (x + 1)(x - 3)
d) x2 - 4x - 3
= x2 - 4x + 4 - 7
= (x + 2)2 - 7
= \(\left(x+2-\sqrt{7}\right)\left(x+2+\sqrt{7}\right)\)
b = x.(x2 + 6x + 9 - 4y2 ) =x.((x+3)2 -4y2 )= x.(x+3-2y).(x+3+2y)
c = (x2 - 2x)+(2y-xy) = x.(x-2) +y.(2-x)= x.(x-2) + y.(-x+2)= x.(x-2) - y.(x-2) = (x-y).(x-2)
d = (x2 +1)2 - 4x2 = (x2 + 1 - 2x).(x2 +1 +2x) = (x-1)2 . (x+1)2
a = (7x)2 - (0.5y)2 = (7x - 0,5y).(7x+0,5y)
Bài 1: 4a2-4ab+b2-9a2b2
=(2a)2-2.2a.b+b2-(3ab)2
=(2a-b)2-(3ab)2
=(2a-b-3ab)(2a-b+3ab)
a/ (4a2-4ab+b2)-9a2b2
= (2a-b)2-(3ab)2
= (2a-b-3ab) (2a-b+3ab)
a) \(4a^2-4a+1-b^2=\left(2a\right)^2-2.2.a+1-b^2\\ =\left(2a-1\right)-b^2=\left(2a-1+b\right)\left(2a-1-b\right)\)
b) \(4x^3-4x^2-9x+9=4x^2\left(x-1\right)-9\left(x-1\right)\\ =\left(x-1\right)\left(4x^2-3^2\right)=\left(x-1\right)\left(2x-3\right)\left(2x+3\right)\)
a, 4x2 - 12x + 9
= (2x + 3)2
b, 9x4y3 + 3x2y4
= 3x2y3(3x2 + y)
c, ( x - 3 )2 - 2x ( x - 3 )
= (x - 3)(x - 3 - 2x)
= (x - 3)(-x - 3)
d, 3x ( x - 1 ) + 6 ( x - 1 )
= 3(x - 1)(x + 2)
e, 2x ( x + 1 ) - 4x - 4
= 2x(x + 1) - 4(x + 1)
= (x + 1)(2x - 4)
= 2(x + 1)(x - 2)
f, ( 2x - 3 )2 - 4x + 6
= (2x - 3)2 - 2(2x - 3)
= (2x - 3)(2x - 3 - 2)
= (2x - 3)(2x - 5)
b,\(4x^3-4x^2-9x+9\)
\(=\left(4x^3-4x^2\right)+\left(-9x+9\right)\)
\(=4x^2\left(x-1\right)-9\left(x-1\right)\)
\(=\left(4x^2-9\right)\left(x-1\right)\)
c,\(xy-x^2+x-y\)
\(=\left(xy-y\right)+\left(-x^2+x\right)\)
\(=y\left(x-1\right)-x\left(x-1\right)\)
\(=\left(y-x\right)\left(x-1\right)\)
Câu a đề kì kì sao á.
\(4a^2-4a+1-b^2\)
=\(\left(4a^2-4a+1\right)-b^2\)
=\(\left(2a-1\right)^2-b^2\)
=\(\left(2a-1-b\right)\left(2a-1+b\right)\)
\(4x^3-4x^2-9x+9\)
=\(\left(4x^3-4x^2\right)-\left(9x-9\right)\)
=\(4x^2\left(x-1\right)-9\left(x-1\right)\)
=\(\left(x-1\right)\left(4x^2-9\right)\)
=\(\left(x-1\right)\left(2x-3\right)\left(2x+3\right)\)
\(xy-x^2+x-y\)
=\(x\left(y-x\right)+\left(x-y\right)\)
=\(x\left(y-x\right)-\left(y-x\right)\)
=\(\left(y-x\right)\left(x-1\right)\)
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