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1.
\(\frac{25x^4y^3-15x^3y^5+20x^2y^4}{5x^2y^3}\)
\(=\frac{5x^2y^3\left(5x^2-3xy^2+4y\right)}{5x^2y^3}\)
\(=5x^2-3xy^2+4y\)
2.
a) \(27x^4-8x=x\left(27x^3-8\right)\)
\(=x\left(3x-2\right)\left(9x^2+6x+4\right)\)
b) \(16x^2y-4xy^2-4x^3+x^2y\)
\(=4xy\left(4x-y\right)-x^2\left(4x-y\right)\)
\(=x\left(4x-y\right)\left(4y-x\right)\)
c) \(x^2-2x-5+2\sqrt{5}\)
\(=\left(x-1\right)^2-6+2\sqrt{5}\)
\(=\left(x-1\right)^2-\left(6-2\sqrt{5}\right)=\left(x-1\right)^2-\left(\sqrt{5}-1\right)^2\)
\(=\left(x-\sqrt{5}\right)\left(x-2+\sqrt{5}\right)\)
Bài 1:
\(\left(25x^4y^3-15x^3y^5+20x^2y^4\right):\left(5x^2y^3\right)\)
\(=\frac{25x^4y^3-15x^3y^5+20x^2y^4}{5x^2y^3}\)
\(=\frac{5x^2y^3\left(5x^2-3xy^2+4y\right)}{5x^2y^3}\)
\(=5x^2-3xy^2+4y\)
Bài 2:
a) \(27x^4-8x\)
\(=x\left(3x-2\right)\left(3^2x^2+2.3x+2^2\right)\)
\(=x\left(3x-2\right)\left(9x^2+6x+4\right)\)
b) \(16x^2y-4xy^2-4x^3+x^2y\)
\(=4y^2+x^2-\left(4x^2\right)^2\)
\(=x\left(-4x^2+xy+4y^2\right)\)
a) 9x4+16y6-24x2y3
=(3x2)2-2.3x2.4y3+(4y3)2
=(3x2-4y3)2
b) 16x2-24xy+9y2
=(4x)2-2.4x.3y+(3y)2
=(4x-3y)2
c) 36x2-(3x-2)2
=(36x-3x+2)(36x+3x-2)
=(33x+2)(39x-2)
d) 27x3+54x2y+36xy2+8y3
=(3x)3+3.(3x)2.2y+3.3x.(2y)2+(2y)3
=(3x+2y)3
e) y9-9x2y6+27x4y3-27x6
=(y3)3-3.(y3)2.3x2+3.y3.(3x2)2-(3x2)3
=(y3-3x2)3
f) 64x3+1
= (4x)3+13
=(4x+1)[(4x)2-4x.1+12]
=(4x+1)(16x2-4x+1)
e) 27x6-8x3 *sửa đề*
=(3x2)3-(2x)3
=(3x2-2x)[(3x)2+3x2.2x+(2x)2]
=(3x2-2x)(9x2+6x3+4x2)
~~~
1/ x^2 +4xy +4y^2 = (x +2y)^2
2/ -x^3 +9x^2 -27x+27= - (x^3 -9x^2+27x-27) = - (x-3)^3
3/ 8x^6 +36x^4y+54^2y^2+27y^3 = (2x^2+3y)^3
4/ x^3 - 6x^2y+12xy^2 -8y^3= (x-2y)^3
d)5.(x-y)-y(x-y)
=(x-y)(5-y)
e) y.(x-z)+7(z-x)
=y.(x-z)-7(x-z)
=(x-z)(y-7)
1, \(3x^2y^2-6x^2y^3+9x^2y^2\)
\(\Leftrightarrow12x^2y^2-6x^2y^2\)
\(\Leftrightarrow3x^2y^2\left(4+2y\right)\)
5x^2y^3 - 25x^3y^4 + 10x^3y^3
\(\Leftrightarrow5x^2y^3\left(1-5xy+2x\right)\)
a) \(5x^2y^3-25x^3y^4+10x^3y^3\)
\(=5x^2y^3\left(1-5xy+2x\right)\)
b) \(4x^2+12x+9\)
\(=\left(2x\right)^2+2.2x.3+3^2\)
\(=\left(2x+3\right)^2\)
c) \(11x+11y-x^2-xy\)
\(=11\left(x+y\right)-x\left(x+y\right)\)
\(=\left(x+y\right)\left(11-x\right)\)
d) \(27x^2\left(y-1\right)-9x^3\left(1-y\right)\)
\(=27x^2\left(y-1\right)+9x^3\left(y-1\right)\)
\(=\left(y-1\right)\left(27x^2+9x^3\right)\)
\(=9x^2\left(y-1\right)\left(3+x\right)\)
c/
\(11x+11y-x^2-xy\)
\(=\left(11x-x^2\right)+\left(11y-xy\right)\)
\(=x\left(11-x\right)+y\left(11-x\right)\)
= \(\left(11-x\right)\left(x+y\right)\)
a: 2x^2y-50xy=2xy(x-25)
b: 5x^2-10x=5x(x-2)
c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)
d: \(x^2-xy+x=x\left(x-y+1\right)\)
e: x(x-y)-2(y-x)
=x(x-y)+2(x-y)
=(x-y)(x+2)
f: 4x^2-4xy-8y^2
=4(x^2-xy-2y^2)
=4(x^2-2xy+xy-2y^2)
=4[x(x-2y)+y(x-2y)]
=4(x-2y)(x+y)
f1: x^2ỹ-y^2+y
=(x-y)(x+y)+(x+y)
=(x+y)(x-y+1)
Lần sau bạn chú ý ghi đầy đủ yêu cầu đề.
Lời giải:
1. $9x^2+4+12x=(3x)^2+2.3x.2+2^2=(3x+2)^2$
2. Đề sai sai. Bạn xem lại
3.
$(16x^2-4xy+y^2)(4x+y)=(4x+y)[(4x)^2-4x.y+y^2]$
$=(4x)^3+y^3=64x^3+y^3$
4.
$(5x-7)(25x^2+35x+49)=(5x-7)[(5x)^2+5x.7+7^2]$
$=(5x)^3-7^3=125x^3-343$
\(9x^2+12x+4=\left(3x+2\right)^2\)
\(\left(16x^2-4xy+y^2\right)\cdot\left(4x+y\right)=64x^3+y^3\)
\(\left(5x-7\right)\left(25x^2+35x+49\right)=125x^3-343\)