A) (x2+x)2 +4x2+4x-12
B) x(x+4) (x+6) (x+10) +128
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22 tháng 7 2023
a: (x^2+x)^2+4x^2+4x-12
=(x^2+x)^2+4(x^2+x)-12
=(x^2+x+6)(x^2+x-2)
=(x^2+x+6)(x+2)(x-1)
b: =(x^2+8x)^2+22(x^2+8x)+105+15
=(x^2+8x)^2+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
c: =8x^2+12x-2x-3
=(2x+3)(4x-1)
23 tháng 7 2023
a: =(x^2+x)^2+4(x^2+x)-12
=(x^2+x+6)(x^2+x-2)
=(x^2+x+6)(x+2)(x-1)
b: =(x^2+8x)^2+22(x^2+8x)+120
=(x^2+8x+12)(x^2+8x+10)
=(x+2)(x+6)(x^2+8x+10)
c: =8x^2+12x-2x-3
=(2x+3)(4x-1)
17 tháng 9 2021
1: Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(x^3+54\right)\)
\(=x^3+27-x^3-54\)
=-27
2: Ta có: \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-8x^3+y^3\)
\(=2y^3\)
18 tháng 9 2021
\(1,=x^3+270-x^3-54=-27\\ 2,=8x^3+y^3-8x^3+y^3=2y^3\\ 3,=x^3-3x^2+3x-1-x^3-8+3x^2-48=3x-57\\ 4,=x^3-x-x^3-1=-x-1\\ 5,=8x^3-5\left(8x^3+1\right)=-32x^3-5\\ 6,=27+x^3-27=x^3\\ 7,làm.ở.câu.3\\ 8,=x^3-6x^2+12x-8+6x^2-12x+6-x^3-1+3x\\ =3x-3\)
H9
HT.Phong (9A5)
CTVHS
21 tháng 8 2023
a) \(x^2+4x+4\)
\(=x^2+2\cdot2\cdot x+2^2\)
\(=\left(x+2\right)^2\)
b) \(4x^2-4x+1\)
\(=\left(2x\right)^2-2\cdot2x\cdot1+1^2\)
\(=\left(2x-1\right)^2\)
c) \(x^2-x+\dfrac{1}{4}\)
\(=x^2-2\cdot\dfrac{1}{2}\cdot x+\left(\dfrac{1}{2}\right)^2\)
\(=\left(x-\dfrac{1}{2}\right)^2\)
d) \(4\left(x+y\right)^2-4\left(x+y\right)+1\)
\(=\left[2\left(x+y\right)\right]^2-2\cdot2\left(x+y\right)\cdot1+1^2\)
\(=\left[2\left(x+y\right)-1\right]^2\)
\(=\left(2x+2y-1\right)^2\)
11 tháng 11 2021
\(a,=4x^2+3xy-y^2+4xy-4x^2=7xy-y^2\\ b,=x^2-9-x^3+3x+x^2-3=-x^3+2x^2+3x-12\\ c,=-2x^2+12x-18+5x^2+4x-1=3x^2+16x-19\\ d,=8x^3+1-3x^3+6x^2=5x^3+6x^2+1\\ e,=\left(3x^2+4x+15x+20\right):\left(3x+4\right)\\ =\left(3x+4\right)\left(x+5\right):\left(3x+4\right)\\ =x+5\\ f,=\left(x^3+4x^2-3x+3x^2+12x-9+3x+3\right):\left(x^2+4x-3\right)\\ =\left[\left(x^2+4x-3\right)\left(x+3\right)+3x+3\right]:\left(x^2+4x-3\right)\\ =x+3\left(dư.3x+3\right)\)
C
1
13 tháng 6 2021
`a)(x-6)^2-(x+6)^2=12`
`<=>(x-6-x-6)(x-6+x+6)=12`
`<=>-12.2x=12`
`<=>2x=-1`
`<=>x=-1/2`
Vậy `x=-1/2`
`b)36x^2-12x+1=81`
`<=>(6x-1)^2=81`
`<=>(6x-1-9)(6x-1+9)=0`
`<=>(6x-10)(6x+8)=0`
`<=>(3x-5)(3x+4)=0`
`<=>` \(\left[ \begin{array}{l}x=\dfrac53\\x=-\dfrac43\end{array} \right.\)
`c)x^2-4x-12=0`
`<=>x^2-6x+2x-12=0`
`<=>x(x-6)+2(x-6)=0`
`<=>(x-6)(x+2)=0`
`<=>` \(\left[ \begin{array}{l}x=-2\\x=6\end{array} \right.\)
`d)x^2-5x-6=0`
`<=>x^2-6x+x-6=0`
`<=>x(x-6)+x-6=0`
`<=>(x-6)(x+1)=0`
`<=>` \(\left[ \begin{array}{l}x=6\\x=-1\end{array} \right.\)
25 tháng 3 2020
Bài 1:
a) (3x - 2)(4x + 5) = 0
<=> 3x - 2 = 0 hoặc 4x + 5 = 0
<=> 3x = 2 hoặc 4x = -5
<=> x = 2/3 hoặc x = -5/4
b) (2,3x - 6,9)(0,1x + 2) = 0
<=> 2,3x - 6,9 = 0 hoặc 0,1x + 2 = 0
<=> 2,3x = 6,9 hoặc 0,1x = -2
<=> x = 3 hoặc x = -20
c) (4x + 2)(x^2 + 1) = 0
<=> 4x + 2 = 0 hoặc x^2 + 1 # 0
<=> 4x = -2
<=> x = -2/4 = -1/2
d) (2x + 7)(x - 5)(5x + 1) = 0
<=> 2x + 7 = 0 hoặc x - 5 = 0 hoặc 5x + 1 = 0
<=> 2x = -7 hoặc x = 5 hoặc 5x = -1
<=> x = -7/2 hoặc x = 5 hoặc x = -1/5
DD
1
ND
Nguyễn Đức Trí
VIP
3 tháng 8 2023
a) \(\left(2x-1\right)^3-4x^2\left(2x-3\right)=5\)
\(\Leftrightarrow8x^3-12x^2+6x-1-8x^3+12x^2=5\)
\(\Leftrightarrow6x-1=5\Leftrightarrow6x=6\Leftrightarrow x=1\)
b) \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x+1\right)^2=-10\)
\(\Leftrightarrow\left(x+1-x+1\right)\left[\left(x^2+2x+1+x^2-2x+1+\left(x^2-1\right)\right)\right]-6\left(x^2+2x+1\right)=-10\)
\(\Leftrightarrow2\left(3x^2+1\right)-6x^2-12x-6=-10\)
\(\Leftrightarrow6x^2+2-6x^2-12x-6=-10\)
\(\Leftrightarrow-12x-4=-10\Leftrightarrow12x=-6\Leftrightarrow x=\dfrac{1}{2}\)
\(B=\left[x\left(x+10\right)\right].\left[\left(x+4\right)\left(x+6\right)\right]+128=\left(x^2+10x\right)\left(x^2+4x+6x+24\right)+128\)
\(=\left(x^2+10x\right)\left(x^2+10x+24\right)+128\)
Đặt\(a=x^2+10x\Rightarrow a+24=x^2+10x+24\)
\(\Rightarrow B=a.\left(a+24\right)+128=a^2+24a+128=a^2+8a+16a+128\)
\(=a\left(a+8\right)+16\left(a+8\right)=\left(a+8\right)\left(a+16\right)=\left(x^2+10x+8\right)\left(x^2+10x+16\right)\)
\(=\left(x^2+10x+8\right)\left(x^2+2x+8x+16\right)=\left(x^2+10x+8\right)\left[x\left(x+2\right)+8\left(x+2\right)\right]\)
\(=\left(x+2\right)\left(x+8\right)\left(x^2+10x+8\right)\)
Xong hết !!!!!!!!!!
______CHÚC BẠN HỌC TỐT_________________
\(A=x^4+2x^3+x^2+4x^2+4x-12=x^4+2x^3+5x^2+4x-12\)
\(=x^4-x^3+3x^3-3x^2+8x^2-8x+12x-12\)
\(=x^3\left(x-1\right)+3x^2\left(x-1\right)+8x\left(x-1\right)+12\left(x-1\right)=\left(x-1\right)\left(x^3+3x^2+8x+12\right)\)
\(=\left(x-1\right)\left(x^3+2x^2+x^2+2x+6x+12\right)=\left(x-1\right)\left[x^2\left(x+1\right)+x\left(x+2\right)+6\left(x+2\right)\right]\)\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)
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