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B2: a) \(\left(x+\dfrac{1}{2}\right)\left(\dfrac{1}{2}-x\right)\)
\(=-\left(x+\dfrac{1}{2}\right)\left(x-\dfrac{1}{2}\right)\)
\(=-x^2+\dfrac{1}{4}\)
b) \(\left(3x-2y\right)\left(3x+2y\right)\)
\(=\left(3x\right)^2-\left(2y\right)^2\)
\(=9x^2-4y^2\)
c) \(\left(x-3\right)\left(3+x\right)\)
\(=x^2-3^2\)
\(=x^2-9\)
d) \(x^2+6x+9\)
\(=x^2+2\cdot3\cdot x+3^2\)
\(=\left(x+3\right)^2\)
e) \(9x^2-6x+1\)
\(=\left(3x\right)^2-2\cdot3x\cdot1+1^2\)
\(=\left(3x-1\right)^2\)
f) \(x^2y^2+xy+\dfrac{1}{4}\)
\(=\left(xy\right)^2+2\cdot\dfrac{1}{2}\cdot xy+\left(\dfrac{1}{2}\right)^2\)
\(=\left(xy+\dfrac{1}{2}\right)^2\)
g) \(\left(x-y\right)^2+6\left(x-y\right)+9\)
\(=\left(x-y\right)^2+2\cdot3\cdot\left(x-y\right)+3^2\)
\(=\left(x-y+3\right)^2\)
h) \(x^2+8x+16\)
\(=x^2+2\cdot4\cdot x+4^2\)
\(=\left(x+4\right)^2\)
i) \(9x^2-24x+16\)
\(=\left(3x\right)^2-2\cdot3x\cdot4+4^2\)
\(=\left(3x-4\right)^2\)
k) \(x^2-3x+\dfrac{9}{4}\)
\(=x^2-2\cdot\dfrac{3}{2}\cdot x+\left(\dfrac{3}{2}\right)^2\)
\(=\left(x-\dfrac{3}{2}\right)^2\)
l) \(4x^2y^4-4xy^3+y^2\)
\(=\left(2xy^2\right)^2-2\cdot2xy^2\cdot y+y^2\)
\(=\left(2xy^2-y\right)^2\)
m) \(9x^2-6x+1\)
\(=\left(3x\right)^2-2\cdot3x\cdot1+1\)
\(=\left(3x-1\right)^2\)
19. 3x2-4x+1
= 3x2-3x-x+1
= (3x2-3x)-(x-1)
= 3x(x-1)-(x-1)
= (3x-1)(x-1)
20.3x2+4x-7
= 3x2+3x-7x-7
= (3x2+3x)-(7x+7)
= 3x(x+1)-7(x-1)
= (3x-7)(x-1)
21.3x2+7x-6
= 3x2+9x-2x-6
= (3x2+9x)-(2x+6)
= 3x(x+3)-2(x+3)
= (3x-2)(x+3)
22.3x2+3x-6
= 3x2+6x-3x-6
=(3x2+6x)-(3x+6)
= 3x(x+2)-3(x+2)
=(3x-3)(x+2)
= 3(x-1)(x+2)
23. 3x2-3x-6
=(3x2-6x)+(3x-6)
=3x(x-2)+3(x-2)
=(3x+3)(x-2)
= 3(x+1)(x-2)
24.6x2-13x+6
= 6x2-9x-4x+6
= (6x2-9x)-(4x-6)
=3x(2x-3)-2(2x-3)
=(3x-2)(2x-3)
25.6x2+13x+6
= 6x2+9x+4x+6
= (6x2+9x)+(4x+6)
=3x(2x+3)+2(2x+3)
=(3x+2)(2x+3)
26. 6x2+15x+6
= (6x2+12x)+(3x+6)
= 6x(x+2)+3(x+2)
=(6x+3)(x+2)
=3(2x+1)(x+2)
27. 6x2-15x+6
= (6x2-12x)-(3x-6)
= 6x(x-2)-3(x-2)
=(6x-3)(x-2)
=3(2x-1)(x-2)
28. 6x2+20x+6
= (6x2+18x)+(2x+6)
= 6x(x+3)+2(x+3)
= (6x+2)(x+3)
= 2(3x+1)(x+3)
29.6x2-20x+6
= (6x2-18x)-(2x-6)
= 6x(x-3)+2(x-3)
= (6x-2)(x-3)
= 2(3x-1)(x-3)
30.6x2+12x+6
= (6x2+6x)+(6x+6)
= 6x(x+1)+6(x+1)
= (6x+6)(x+1)
= 6(x+1)(x+1)
= 6(x+1)2
Oxit bazo :
ZnO : Kẽm oxit
Fe2O3 : Sắt III oxit
CaO : Canxi oxit
Oxit axit :
CO2 : Cacbon dioxit
SO2 : Lưu huỳnh đioxit