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Câu 3 ( Đề 1)
a) A = ( x - 2)2 - ( x + 3)( x - 3)
A = x2 - 4x + 4 - x2 + 9
A = - 4x + 13
b) B = 4x( x + 3) - 3x(4 + x)
B = 4x2 + 12x - 12x - 3x2
B = x2
Câu 4 . a) 5x3 - 45x
= 5x( x2 - 32)
= 5x( x - 3)( x + 3)
b) 5x2 + 5xy - x - y
= 5x( x + y) - ( x +y)
= ( x + y)( 5x - 1)
c) x3 - 9x2y + xy2 - 9y3
= x( x2 + y2) - 9y( x2 + y2)
= ( x2 + y2)( x - 9y)
Câu 3 : ( đề 2)
a) A = ( x - 2)2 -( x + 1)( x - 1) - x( 1 - x)
A= x2 - 4x + 4 - x2 + 1 - x + x2
A = x2 - 5x + 5
b)B = 7x( x - 4) - 2x( x - 6)
B = 7x2 - 28x - 2x2 + 12x
B = 5x2 - 16x
Cau 4 .
a) 4x3 - 64x
= 4x( x2 - 42)
= 4x( x - 4)( x + 4)
b) x3 + x + 5x2 + 5
= x( x2 + 1) + 5( x2 + 1)
= ( x2 + 1)( x + 5)
c) x2 - 3xy - 10y2
= x2 - (2y)2 - 3xy - 6y2
= ( x - 2y)( x + 2y) - 3y( x + 2y)
= ( x + 2y)( x - 5y)
Cau 5 . 4x2 - 5x + x3 - 20
= x2( x + 4) - 5( x + 4)
= ( x + 4)( x2 - 5)
Vay phep chia : ( 4x2 - 5x + x3 - 20) cho da thuc ( x + 4) duoc thuong la x2 - 5
bài 4
a) 4x3-64x
= 4x(x2-16)
b)x3+x+5x2+5
= (x3+x)+(5x2+5)
= x(x2+1)+5(x2+1)
= (x2+1)(x+5)
18, \(\frac{x}{2}+\frac{x^2}{8}=0\Leftrightarrow4x+x^2=0\Leftrightarrow x\left(x+4\right)=0\Leftrightarrow x=-4;x=0\)
19, \(4-x=2\left(x-4\right)^2\Leftrightarrow\left(4-x\right)-2\left(4-x\right)^2=0\)
\(\Leftrightarrow\left(4-x\right)\left[1-2\left(4-x\right)\right]=0\Leftrightarrow\left(4-x\right)\left(-7+2x\right)=0\Leftrightarrow x=4;x=\frac{7}{2}\)
20, \(\left(x^2+1\right)\left(x-2\right)+2x-4=0\Leftrightarrow\left(x^2+1\right)\left(x-2\right)+2\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2+3>0\right)=0\Leftrightarrow x=2\)
21, \(x^4-16x^2=0\Leftrightarrow x^2\left(x-4\right)\left(x+4\right)=0\Leftrightarrow x=0;x=\pm4\)
22, \(\left(x-5\right)^3-x+5=0\Leftrightarrow\left(x-5\right)^3-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left[\left(x-5\right)^2-1\right]=0\Leftrightarrow\left(x-5\right)\left(x-6\right)\left(x-4\right)=0\Leftrightarrow x=4;x=5;x=6\)
23, \(5\left(x-2\right)-x^2+4=0\Leftrightarrow5\left(x-2\right)-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(5-x-2\right)=0\Leftrightarrow x=2;x=3\)
Bài 1:
\(a,\dfrac{25}{14x^2y}=\dfrac{75y^4}{42x^2y^5};\dfrac{14}{21xy^5}=\dfrac{28x}{42x^2y^5}\\ b,\dfrac{3x+1}{12xy^4}=\dfrac{3x\left(3x+1\right)}{36x^2y^4};\dfrac{y-2}{9x^2y^3}=\dfrac{4y\left(y-2\right)}{36x^2y^4}\\ c,\dfrac{1}{6x^3y^2}=\dfrac{6y^2}{36x^3y^4};\dfrac{x+1}{9x^2y^4}=\dfrac{4x\left(x+1\right)}{36x^3y^4};\dfrac{x-1}{4xy^3}=\dfrac{9x^2y\left(x-1\right)}{36x^3y^4}\\ d,\dfrac{3+2x}{10x^4y}=\dfrac{12y^4\left(3+2x\right)}{120x^4y^5};\dfrac{5}{8x^2y^2}=\dfrac{75x^2y^3}{120x^4y^5};\dfrac{2}{3xy^5}=\dfrac{80x^3}{120x^4y^5}\)