phân tích đa thức thành nhân tử: 24x2-6+36y-54y2
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DT
2
H9
HT.Phong (9A5)
CTVHS
21 tháng 11 2023
\(-4x^2-24xy-36y^2\)
\(=-\left(4x^2+24xy+36y^2\right)\)
\(=-\left[\left(2x\right)^2+24xy+\left(6y\right)^2\right]\)
\(=-\left[\left(2x\right)^2+2\cdot2x\cdot6y+\left(6y\right)^2\right]\)
\(=-\left(2x+6y\right)^2\)
\(=-\left[2\left(x+3y\right)\right]^2\)
\(=-4\left(x+3y\right)^2\)
NX
3
30 tháng 10 2018
\(=\left(12x+9x^2+4\right)-\left(6y\right)^2=\left(3x+2\right)^2-\left(6y\right)^2\)
\(=\left(3x+2-6y\right)\left(3x+2+6y\right)\)
k mình cái
30 tháng 10 2018
12x+9x2+4-36y2
= (9x2+12x+4)-36y2
= (3x+2)2-36y2
= ((3x+2)-6y2)((3x+2)+6y2)
=(3x+2-6y2)(3x+2+6y2)
MH
22 tháng 10 2021
a) \(24x^2-4xy\)
\(=4x\left(6x-y\right)\)
b) \(5x^3-10x^2+5x-20xy^2\)
\(=5x\left(x^2-10x+5-20y^2\right)\)
7 tháng 11 2018
a) \(x^6-y^6\)
\(=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
b) \(10ab+0,25a^2+100b^2\)
\(=\left(0,5a\right)^2+2\cdot0,5a\cdot10b+\left(10b\right)^2\)
\(=\left(0,5a+10b\right)^2\)
c) \(9x^2-xy+\frac{1}{36}y^2\)
\(=\left(3x\right)^2-2\cdot3x\cdot\frac{1}{6}y+\left(\frac{1}{6}y\right)^2\)
\(=\left(3x-\frac{1}{6}y\right)^2\)
NT
2
20 tháng 10 2018
\(49\left(y-4\right)^2-9y^2-36y-36\)
\(=\left[7\left(y-4\right)\right]^2-\left[\left(3y\right)^2+2.3y.6+6^2\right]\)
\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)
\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)=\left(4y-34\right)\left(10y-22\right)=4\left(2y-17\right)\left(5y-11\right)\)
20 tháng 10 2018
\(49\left(y-4\right)^2-9y^2-36y-36=49\left(y-4\right)^2-9\left(y^2+4y+4\right)\)\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y+4\right)\right]^2=\left(7y-28-3y-12\right)\left(7y-28+3y+12\right)\)\(=\left(4y-40\right)\left(10y-16\right)=4\left(y-20\right)\left(5y-8\right)\)
OO
1
PH
0
H9
HT.Phong (9A5)
CTVHS
4 tháng 9 2023
a) \(2x^2+5x+2\)
\(=2x^2+4x+x+2\)
\(=2x\left(x+2\right)+\left(x+2\right)\)
\(=\left(x+2\right)\left(2x+1\right)\)
b) \(4x^2-4x-9y^2+12y-3\)
\(=\left(4x^2-4x+1\right)-\left(9y^2-12y+4\right)\)
\(=\left(2x-1\right)^2-\left(3y-2\right)^2\)
\(=\left(2x-1+3y-2\right)\left(2x-1-3y+2\right)\)
\(=\left(2x+3y-3\right)\left(2x-3y+1\right)\)
c) \(x^4-2x^3-4x^2+4x-3\)
\(=x^4+x^3-x^2+x-3x^2-3x+3x-3\)
\(=\left(x^4+x^3-x^2+x\right)-\left(3x^2+3x-3x+3\right)\)
\(=x\left(x^3+x^2-x+1\right)-3\left(x^3+x^2-x+1\right)\)
\(=\left(x^3+x^2-x+1\right)\left(x-3\right)\)
d) \(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)
18 tháng 10 2021
b: \(8x^2-48x+6xy-36y\)
\(=8x\left(x-6\right)+6y\left(x-6\right)\)
\(=2\left(x-6\right)\left(4x+3y\right)\)
d: \(a^2-2ab+b^2-4\)
\(=\left(a-b\right)^2-4\)
\(=\left(a-b-2\right)\left(a-b+2\right)\)
\(=6\left(4x^2-9y^2+6y-1\right)\)
\(=6\left[\left(2x\right)^2-\left(3y-1\right)^2\right]\)
\(=6\left(2x-3y+1\right)\left(2x+3y-1\right)\)
\(24x^2+36y-54y^2-6\)
\(=6\left(4x^2+6y-9y^2-1\right)\)
\(=6\left[4x^2-\left(9y^2-6y+1\right)\right]\)
\(=6\cdot\left[\left(2x\right)^2-\left(3y-1\right)^2\right]\)
\(=6\left(2x-3y+1\right)\left(2x+3y-1\right)\)