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a) x2-y2-2x+2y
=(x+y)(x-y)-2(x-y)
=(x-y)(x+y-2)
b) 2x + 2y - x2 -xy
=2(x+y) - x(x+y)
=(x+y)(2-x)
c) 3a2 - 6ab + 3b2 - 12c2
= 3(a2+b2) -3(2ab+4c2)
= 3(a2+b2-2ab-4c2)
d) x2 - 25 + y2 + 2xy
= x2 + 2xy + y2 -25
= (x+y)2 - 52
= (x+y+5)(x+y-5)
e) x2y - x3 - 9y + 9x
= (9x - x3)+(x2y -9y)
= x(9-x2)+y(x2 - 9)
= x(9-x2)-y(9-x2)
= (9-x2)(x-y)
f) x2-2x-4y2-4y
= x2-4y2-2(x+2y)
=(x+2y)(x-4y)-2(x+2y)
=(x+2y)(x-4y-2)
câu g trùng với câu e
h) x2(x-1)+16(1-x)
= x2(x-1)-16(x-1)
= (x2-16)(x-1)
= (x+4)(x-4)(x-1)
\(=\dfrac{2y+x}{y\left(2y-x\right)}+\dfrac{8x}{\left(x-2y\right)\left(x+2y\right)}+\dfrac{2y-x}{y\left(2y+x\right)}\)
\(=\dfrac{2y+x}{y\left(2y-x\right)}-\dfrac{8x}{\left(2y-x\right)\left(x+2y\right)}+\dfrac{2y-x}{y\left(2y+x\right)}\)
\(=\dfrac{\left(2y+x\right)^2}{y\left(2y-x\right)\left(2y+x\right)}-\dfrac{8xy}{y\left(2y-x\right)\left(x+2y\right)}+\dfrac{\left(2y-x\right)^2}{y\left(2y+x\right)\left(2y-x\right)}\)
\(=\dfrac{\left(2y+x\right)^2-8xy+\left(2y-x\right)^2}{y\left(2y-x\right)\left(2y+x\right)}\)
\(=\dfrac{8y^2-8xy+2x^2}{\left(y\right)\left(2y-x\right)\left(2y+x\right)}\)
Phân tích trên tử ta có:
\(=2\left(\left(2y\right)^2+4xy+x^2\right)=2\left(2y+x\right)^2\)
\(=\dfrac{2\left(2y+x\right)^2}{y\left(2y+x\right)\left(2y-x\right)}=\dfrac{2\left(2y+x\right)}{y\left(2y-x\right)}\)
CHÚC BẠN HỌC TỐT......
-(a - 3)2 = -(a2 - 6a + 9) = -a2 + 6a - 9
(x - 2)(x + 2) = x2 - 4
-(5 + 4y)(5 - 4y) = -(25 - 16y2) = -25 + 16y2
(\(\dfrac{1}{2}\)x + 2y)(\(\dfrac{1}{2}\)x - 2y) = \(\dfrac{1}{4}\)x2 - 4y2
a) \(\frac{6xy+4y}{4x^2y^2}+\frac{2xy-4y}{4x^2y^2}\)
\(=\frac{6xy+4y+2xy-4y}{4x^2y^2}\)
\(=\frac{8xy}{4x^2y^2}\)
\(=\frac{2}{xy}\)
b) \(\frac{5}{x+3}-\frac{3}{x-3}+\frac{30}{x^2-9}\)
\(=\frac{5\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\frac{3\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{30}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{5x-15-3x-9+30}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{2x+6}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{2\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{2}{x-3}\)
c) \(\frac{2x+8}{\left(x+2\right)^2}:\frac{x+4}{x+2}\)
\(=\frac{2\left(x+4\right)}{\left(x+2\right)^2}\cdot\frac{x+2}{x+4}\)
\(=\frac{2\left(x+4\right)\left(x+2\right)}{\left(x+2\right)\left(x+2\right)\left(x+4\right)}\)
\(=\frac{2}{x+2}\)
a, \(\frac{x+2y}{8x^2y^5}-\frac{3x^2+2}{12x^4y^4}\)
=\(\frac{\left(x+2y\right)3x^2}{24x^4y^5}-\frac{\left(3x^2+2\right)2y}{24x^4y^5}\)
=\(\frac{3x^3+6x^2y}{24x^4y^5}-\frac{6x^2y+4y}{24x^4y^5}\)
=\(\frac{3x^3+6x^2y-6x^2y-4y}{24x^4y^5}\)
=\(\frac{3x^3-4y}{24x^4y^5}\)
b,\(\frac{y}{xy-5x^2}-\frac{15y-25x}{y^2-25x^2}\)
=\(\frac{y}{x\left(y-5x\right)}-\frac{15y-25x}{\left(y-5x\right)\left(y+5x\right)}\)
=\(\frac{y\left(y+5x\right)}{x\left(y-5x\right)\left(y+5x\right)}-\frac{\left(15y-25x\right)x}{x\left(y-5x\right)\left(y+5x\right)}\)
=\(\frac{y^2+5xy}{x\left(y-5x\right)\left(y+5x\right)}-\frac{15xy-25x^2}{x\left(y-5x\right)\left(y+5x\right)}\)
=\(\frac{y^2+5xy-15xy+25x^2}{x\left(y-5x\right)\left(y+5x\right)}\)
=\(\frac{y^2-10xy+25x^2}{x\left(y-5x\right)\left(y+5x\right)}\)
=\(\frac{\left(y-5x\right)^2}{x\left(y-5x\right)\left(y+5x\right)}\)
=\(\frac{y-5x}{x\left(y+5x\right)}\)
c,\(\frac{4-x}{x^3+2x}-\frac{x+5}{x^3-x^2+2x-2}\)
=\(\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{\left(x^3-x^2\right)+\left(2x-2\right)}\)
=\(\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{x^2\left(x-1\right)+2\left(x-1\right)}\)
=\(\frac{4-x}{x\left(x^2+2\right)}-\frac{x+5}{\left(x-1\right)\left(x^2+2\right)}\)
=\(\frac{\left(4-x\right)\left(x-1\right)}{x\left(x-1\right)\left(x^2+2\right)}-\frac{\left(x+5\right)x}{x\left(x-1\right)\left(x^2+2\right)}\)
=\(\frac{4x-4-x^2+x}{x\left(x-1\right)\left(x^2+2\right)}-\frac{x^2+5x}{x\left(x-1\right)\left(x^2+2\right)}\)
=\(\frac{4x-4-x^2+x-x^2-5x}{x\left(x-1\right)\left(x^2+2\right)}\)
=\(\frac{-2x^2-4}{x\left(x-1\right)\left(x^2+2\right)}\)
=\(\frac{-2\left(x^2+2\right)}{x\left(x-1\right)\left(x^2+2\right)}\)
=\(\frac{-2}{x\left(x-1\right)}\)
\(C=x^2+4y^2-2x+10+4xy-4y\)
\(=\left(x^2+4xy+4y^2\right)-2\left(x+2y\right)+10\)
\(=5^2-2\cdot5+10=25-10+10=25\)
(2y+x)(x-2y)
\(=2y.x+2y.\left(-2y\right)+x.x+x.\left(-2y\right)=2xy-4y^2+x^2-2xy=x^2-4y^2\)
Chọn A bạn nhé
A