phân tích đa thức thành nhân tử = pp bổ sung hằng đẳng thức:
\(x^2-2.x.\frac{1}{2}+\left(\frac{1}{2}\right)^2-\frac{9}{4}\)
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Khách
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Những câu hỏi liên quan
21 tháng 7 2019
\(\left(2x+1\right)^2-\left(x-1\right)^2=\left(2x+1-x+1\right)\left(2x+1+x-1\right)=\left(x+2\right)3x\)
21 tháng 7 2019
TL:
\(\left(2x+1\right)^2-\left(x-1\right)^2\)
\(=\left(2x+1+x-1\right)\left(2x+1-x+1\right)\)
\(=3x.\left(x+2\right)\)
16 tháng 8 2017
a) \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}=\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)
b) \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{1}{4}-2=\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)
DH
16 tháng 8 2017
a, \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)
\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{2}^2\)
\(=\left(x-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{3}{2}\right)\)
\(=\left(x-2\right)\left(x+1\right)\)
b, \(x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{1}{4}-2\)
\(=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{9}{4}\)
\(=\left(x-\dfrac{1}{2}\right)^2-\dfrac{3}{2}^2\)
\(=\left(x-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{3}{2}\right)\)
\(=\left(x-2\right)\left(x+1\right)\)
Chúc bạn học tốt!!!
17 tháng 12 2019
\(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)
\(=\frac{2}{xy}:\left(\frac{y-x}{xy}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)
\(=\frac{2}{xy}:\frac{\left(x-y\right)^2}{x^2y^2}-\frac{x^2+y^2}{\left(x-y\right)^2}\)
\(=\frac{2x^2y^2}{xy\left(x-y\right)^2}-\frac{x^2+y^2}{\left(x-y\right)^2}\)
\(=\frac{2xy}{\left(x-y\right)^2}-\frac{x^2+y^2}{\left(x-y\right)^2}=\frac{-x^2+2xy-y^2}{\left(x-y\right)^2}\)
\(=-\frac{\left(x-y\right)^2}{\left(x-y\right)^2}=-1\)
24 tháng 8 2023
a: =4x^2+8x-3x-6
=4x(x+2)-3(x+2)
=(x+2)(4x-3)
b: =3(3x^2-2x-1)
=3(3x^2-3x+x-1)
=3(x-1)(3x+1)
c: =2x^2-4x+x-2
=2x(x-2)+(x-2)
=(x-2)(2x+1)
d: =3x^2+3x-2x-2
=3x(x+1)-2(x+1)
=(x+1)(3x-2)
e: =3x^2+9x+x+3
=3x(x+3)+(x+3)
=(x+3)(3x+1)
H9
HT.Phong (9A5)
CTVHS
24 tháng 8 2023
a) \(4x^2+5x-6\)
\(=4x^2+8x-3x-6\)
\(=\left(4x^2+8x\right)-\left(3x+6\right)\)
\(=4x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(4x-3\right)\)
b) \(9x^2-6x-3\)
\(=3\left(3x^2-2x-1\right)\)
\(=3\left(3x^2-3x+x-1\right)\)
\(=3\left[3x\left(x-1\right)+\left(x-1\right)\right]\)
\(=3\left(x-1\right)\left(3x+1\right)\)
c) \(2x^2-3x-2\)
\(=2x^2-4x+x-2\)
\(=\left(2x^2-4x\right)+\left(x-2\right)\)
\(=2x\left(x-2\right)+\left(x-2\right)\)
\(=\left(2x+1\right)\left(x-2\right)\)
d) \(3x^2+x-2\)
\(=3x^2+3x-2x-2\)
\(=\left(3x^2+3x\right)-\left(2x+2\right)\)
\(=3x\left(x+1\right)-2\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-2\right)\)
e) \(3x^2+10x+3\)
\(=3x^2+9x+x+3\)
\(=3x\left(x+3\right)+\left(x+3\right)\)
\(=\left(x+3\right)\left(3x+1\right)\)
D
22 tháng 7 2018
\(1,\)
\(x^2+x-12\)
\(=x^2-3x+4x-12\)
\(=x\left(x-3\right)+4\left(x-3\right)\)
\(=\left(x+4\right)\left(x-3\right)\)
\(2,\)
\(x^2-9x+20\)
\(=x^2-4x-5x+20\)
\(=x\left(x-4\right)-5\left(x-4\right)\)
\(=\left(x-5\right)\left(x-4\right)\)
\(3,\)
\(x^2+x-20\)
\(=x^2-4x+5x-20\)
\(=x\left(x-4\right)+5\left(x-4\right)\)
\(=\left(x+5\right)\left(x-4\right)\)
21 tháng 8 2016
c ) \(x^2-7x+12\)
\(=\left(x^2-3x\right)-\left(4x-12\right)\)
\(=x\left(x-3\right)-4\left(x-3\right)\)
\(=\left(x-4\right)\left(x-3\right)\)
d ) \(x^2+7x+12\)
\(=\left(x^2+3x\right)+\left(4x+12\right)\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+4\right)\left(x+3\right)\)
21 tháng 8 2016
a ) \(x^2-5x+6\)
\(=\left(x^2-2x\right)-\left(3x-6\right)\)
\(=x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x-2\right)\left(x-3\right)\)
b )\(x^2+5x+6\)
\(=\left(x^2+2x\right)+\left(3x+6\right)\)
\(=x\left(x+2\right)+3\left(x+2\right)\)
\(=\left(x+2\right)\left(x+3\right)\)
21 tháng 8 2016
a.x^2 - 5x + 6
=x2-2x-3x+6
=x(x-2)-3(x-2)
=(x-3)(x-2)
b.x^2 + 5x + 6
=x2+3x+2x+6
=x(x+3)+2(x+3)
=(x+2)(x+3)
10 tháng 10 2018
a) 9 -(x-y)2
= 32 - (x-y)2
= (3-x+y).(3+x-y)
b) (x2 +4)2 - 16x2
= (x2+4)2 - (4x)2
= (x2 + 4 -4x).(x2 + 4 +4x)
10 tháng 10 2018
\(9-\left(x-y\right)^2\)
\(=3^2-\left(x-y\right)^2\)
\(=\left(3-x+y\right)\left(3+x-y\right)\)
\(\left(x^2+4\right)^2-16x^2\)
\(=\left(x^2+4\right)^2-\left(4x\right)^2\)
\(=\left(x^2-4x+4\right)\left(x^2+4x+4\right)\)
\(=\left(x-2\right)^2\left(x+2\right)^2\)
NC
2
27 tháng 10 2014
x2 + x -12 = x2 + 4x - 3x - 12 = x(x+4) - 3(x+4) = (x+4)(x-3)
27 tháng 9 2018
\(x^2+x-12\)
\(=x^2+x+\frac{1}{4}-\frac{49}{4}\)
\(=\left(x+\frac{1}{2}\right)^2-\left(\frac{7}{2}\right)^2\)
\(=\left(x+\frac{1}{2}-\frac{7}{2}\right)\left(x+\frac{1}{2}+\frac{7}{2}\right)\)
\(=\left(x-3\right)\left(x+4\right)\)
x2-2.x.1/2 +(1/2)2-9/4
=(x-1/2)2-9/4
=(x-1/2)2-(3/2)2
=(x-1/2-3/2).(x-1/2+3/2)
=(x-2)(x+1)