Câu 1: Phân tích thành nhân tửa/5a2c – 45b2c + 15bc2 – 5ac2b/3x3y – x2y2 – 3x2yz +xy2z c/(am + bp)2 – (ap +...
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Câu 1: Phân tích thành nhân tử
a/5a2c – 45b2c + 15bc2 – 5ac2
b/3x3y – x2y2 – 3x2yz +xy2z
c/(am + bp)2 – (ap + bm)2
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Bài 3:
b. $B=(x+y)(2x-y)+(xy^4-x^2y^2):(xy^2)$
$=(2x^2-xy+2xy-y^2)+(y^2-x)$
$=2x^2+xy-y^2+y^2-x=2x^2+xy-x$
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Bài 4:
a. $25x^3-10x^2+x=x(25x^2-10x+1)=x(5x-1)^2$
b. $x^2-9x+9y-y^2=(x^2-y^2)-(9x-9y)=(x-y)(x+y)-9(x-y)=(x-y)(x+y-9)$
c. $16-x^2-4y^2-4xy=16-(x^2+4y^2+4xy)$
$=4^2-(x+2y)^2=(4-x-2y)(4+x+2y)$
12 tháng 10 2023
a: \(x^2+4x+4=x^2+2\cdot x\cdot2+2^2=\left(x+2\right)^2\)
b: \(4x^2-4x+1=\left(2x\right)^2-2\cdot2x\cdot1+1^2=\left(2x-1\right)^2\)
c: \(2x-1-x^2\)
\(=-\left(x^2-2x+1\right)=-\left(x-1\right)^2\)
d: \(x^2+x+\dfrac{1}{4}=x^2+2\cdot x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)
e: \(9-x^2=3^2-x^2=\left(3-x\right)\left(3+x\right)\)
g: \(\left(x+5\right)^2-4x^2=\left(x+5+2x\right)\left(x+5-2x\right)\)
\(=\left(5-x\right)\left(5+3x\right)\)
h: \(\left(x+1\right)^2-\left(2x-1\right)^2\)
\(=\left(x+1+2x-1\right)\left(x+1-2x+1\right)\)
\(=3x\left(-x+2\right)\)
i: \(=x^2y^2-4xy+4-3\)
\(=\left(xy-2\right)^2-3=\left(xy-2-\sqrt{3}\right)\left(xy-2+\sqrt{3}\right)\)
k: \(=y^2-\left(x-1\right)^2\)
\(=\left(y-x+1\right)\left(y+x-1\right)\)
l: \(=x^3+3\cdot x^2\cdot2+3\cdot x\cdot2^2+2^3=\left(x+2\right)^3\)
m: \(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2-y^3=\left(2x-y\right)^3\)
LT
1
12 tháng 12 2023
a: \(15a^2x-10ax^2\)
\(=5ax\cdot3a-5ax\cdot2x\)
\(=5ax\left(3a-2x\right)\)
b: \(2xy-4x+5y-10\)
\(=\left(2xy-4x\right)+\left(5y-10\right)\)
\(=2x\left(y-2\right)+5\left(y-2\right)\)
\(=\left(y-2\right)\left(2x+5\right)\)
AM
7 tháng 2 2022
Ta có: \(a\left(x^2+1\right)-x\left(a^2+1\right)=ax^2+a-xa^2-x=ax\left(x-a\right)-\left(x-a\right)=\left(x-a\right)\left(ax-1\right)\)
7 tháng 2 2022
\(=x^2a+a-xa^2-x=x\left(xa-1\right)+a\left(1-xa\right)=\left(x-a\right)\left(xa-1\right)\)
LV
1
PT
1
MN
2
9 tháng 10 2023
a: \(=y\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(y-1\right)\)
b: \(=\left(x^2y^2-8-1\right)\left(x^2y^2-8+1\right)\)
\(=\left(x^2y^2-9\right)\left(x^2y^2-7\right)\)
\(=\left(xy-3\right)\left(xy+3\right)\left(x^2y^2-7\right)\)
c: \(=x^2-8x+x-8\)
\(=x\left(x-8\right)+\left(x-8\right)\)
\(=\left(x-8\right)\left(x+1\right)\)
T
9 tháng 10 2023
\(a,xy+y^2-x-y\)
\(=\left(xy+y^2\right)-\left(x+y\right)\)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(y-1\right)\)
\(---\)
\(b,\left(x^2y^2-8\right)^2-1\)
\(=\left(x^2y^2-8-1\right)\left(x^2y^2-8+1\right)\)
\(=\left[\left(xy\right)^2-9\right]\left(x^2y^2-7\right)\)
\(=\left(xy-3\right)\left(xy+3\right)\left(x^2y^2-7\right)\)
\(---\)
\(c,x^2-7x-8\)
\(=x^2+x-8x-8\)
\(=\left(x^2+x\right)-\left(8x+8\right)\)
\(=x\left(x+1\right)-8\left(x+1\right)\)
\(=\left(x+1\right)\left(x-8\right)\)
\(Toru\)
a)\(=5c\left(a^2-9b^2\right)+5c^2.\left(3b-a\right)\))\
\(=5c\left(a-3b\right)\left(a+3b\right)-5c^2.\left(a-3b\right)\)
= \(5c.\left(a-3b\right)\left(a+3b-c\right)\)
b)\(=xy.\left(3x-y\right)-xyz.\left(3x-y\right)\)
\(=xy.\left(3x-y\right)\left(1-z\right)\)
c) \(=a^2m^2+2ambp+b^2p^2-a^2p^2-2ambp-b^2m^2\)
\(=a^2m^2-a^2p^2+b^2p^2-b^2m^2\)
\(=a^2.\left(m^2-p^2\right)+b^2\left(p^2-m^2\right)\)
\(=a^2.\left(m^2-p^2\right)-b^2\left(m^2-p^2\right)\)
\(=\left(a^2-b^2\right)\left(m^2-p^2\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(m-p\right)\left(m+p\right)\)