a) (x + y)2 - 2(x + y) + 1
= (x + y)2 - 2.1.(x + y) + 1
= (x + y - 1)2
b) x3 + 1 - x2 - x
= (x3 - x2) - (x - 1)
= x2(x - 1) - (x - 1)
= (x2 - 1)(x - 1) = (x - 1)(x + 1)(x - 1) = (x - 1)2(x + 1)
c) 27x3 - 0,001
= \(\left(3x\right)^3-\frac{1}{1000}=\left(3x\right)^3-\left(\frac{1}{10}\right)^3=\left(3x-\frac{1}{10}\right)\left(9x^2+\frac{3}{10}x+\frac{1}{100}\right)\)
d) 125x3 - 1 =(5x)3 - 1 = (5x - 1)(25x2 + 5x + 1)
e) (x2 + 4)2 - 16x2
= (x2 + 4)2 - (4x)2
= (x2 - 4x + 4)(x2 + 4x + 4)
= (x - 2)2(x + 2)2
= [(x - 2)(x + 2)]2
a.\(\left(x+y\right)^2-2\left(x+y\right)+1\)
\(=\left(x+y\right)^2-2.\left(x+y\right).1+1^2\)
\(=\left[\left(x+y\right)-1\right]^2\)
\(=\left(x+y-1\right)^2\)
b.\(x^3+1-x^2-x\)
\(=\left(x^3-x^2\right)+\left(1-x\right)\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)\)
c.\(27x^3-0,001\)
\(=27x^3-\frac{1}{1000}\)
\(=\left(3x\right)^3-\left(\frac{1}{10}\right)^3\)
\(=\left(3x-\frac{1}{10}\right)\left(9x^2+0,3x+\frac{1}{100}\right)\)
d,\(125x^3-1\)
\(=\left(5x\right)^3-1^3\)
\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)
e.\(\left(x^2+4\right)^2-16x^2\)
\(=\left(x^2+4\right)^2-\left(4x\right)^2\)
\(=\left(x^2+4-4x\right)\left(x^2+4+4x\right)\)
\(=\left(x^2-4x+4\right)\left(x^2+4x+4\right)\)
\(=\left(x-2\right)^2\left(x+2\right)^2\)
Trả lời:
a, ( x + y )2 - 2 ( x + y ) + 1
= ( x + y )2 - 2 ( x + y ) . 1 + 12
= ( x + y - 1 )2
b, x3 + 1 - x2 - x
= ( x3 - x2 ) - ( x - 1 )
= x2 ( x - 1 ) - ( x - 1 )
= (x - 1 ) ( x2 - 1 )
= ( x - 1 ) ( x - 1 ) ( x + 1 )
= ( x - 1 )2 ( x + 1 )
c, 27x3 - 0,001
= ( 3x )3 - ( 0,1 )3
= ( 3x - 0,1 ) ( 9x2 + 0,3x + 0,01 )
d, 125x3 - 1
= ( 5x )3 - 13
= ( 5x - 1 ) ( 25x2 + 10x + 1 )
e, ( x2 + 4 )2 - 16x2
= ( x2 + 4 )2 - ( 4x )2
= ( x2 + 4 - 4x ) ( x2 + 4 + 4x )
= ( x - 2 )2 ( x + 2 )2
