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Bài 1
a,=10201 b,39601 c,2491
Bài 2
(2x+3y)^2 +2(3x+3y)+1=(2x+3y+1)^2
Bài `1.`
`a, 101^2=(100+1)^2=100^2 +2.100.1 +1^2=10201`
`b, 199^2=(200-1)^2=200^2 - 2 . 200.1 +1^2=39601`
`c, 47 . 53=(50 - 3)(50+3) = 50^2 - 3^2=2491`
Bài `2.`
`(2x+3y)^2 +2 (2x+3y) +1 = (2x+3y)^2 +2 . (2x+3y).1+1^2=(2x+3y+1)^2`
9x2+4y2+2(3x+2y+6xy)+1
= 9x2+4y2+1+6x+4y+12xy
=(3x)2+(2y)2+12+2.3x.2y+2.2y.1+2.3x.1 (1)
Thay 3x=m,2y=n,1=p
=>(1)=m2+n2+p2+2mn+2np+2pm=(m+n+p)2
=> 9x2+4y2+2(3x+2y+6xy)+1=(3x+2y+1)2
a) x2+6x+9=x2+2.x.3+32=(x+3)2
b) x2+x+\(\dfrac{1}{4}\)=x2+2.x.\(\dfrac{1}{2}\)+\(\dfrac{1}{4}\)=(x+\(\dfrac{1}{2}\))2
c) 2xy2+x2y4+1=(xy2)2+2.xy2+1=(xy2+1)2
f: \(x^2y^2+2xy+1=\left(xy+1\right)^2\)
g: \(\left(3x-2y\right)^2+2\left(3x-2y\right)+1=\left(3x-2y+1\right)^2\)
h: \(\left(x-3y\right)^2-8\left(x-3y\right)+16=\left(x-3y-4\right)^2\)
i: \(\left(x+y\right)^2+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)^2=4x^2\)
\(x^2+2\left(x+1\right)^2+3\left(x+2\right)^2+4\left(x+3\right)^2\)
\(=x^2+2\left(x^2+2x+1\right)+3\left(x^2+4x+4\right)+4\left(x^2+6x+9\right)\)
\(=10x^2+40x+50\)
\(=\left(x^2+10x+25\right)+\left(9x^2+30x+25\right)\)
\(=\left(x+5\right)^2+\left(3x+5\right)^2\)
\(x^2+2\left(x+1\right)^2+3\left(x+2\right)^2+4\left(x+3\right)^2\)
\(=x^2+2\left(x^2+2x+1\right)+3\left(x^2+4x+4\right)+4\left(x^2+6x+9\right)\)
\(=x^2+2x^2+4x+2+3x^2+12x+12+4x^2+24x+36\)
\(=10x^2+40x+50\)
\(=\left(9x^2+30x+25\right)+\left(x^2+10x+25\right)\)
\(=\left(3x+2\right)^2+\left(x+5^2\right)\)
1)
\(=x^2-4x+4+y^2+2y+1\)
\(=\left(x-2\right)^2+\left(y+1\right)^2\)
2)
\(=a^2+2ab+b^2+a^2-2ax+x^2\)
\(=\left(a+b\right)^2+\left(a-x\right)^2\)
3)
\(=x^2-2x+1+y^2+6y+9\)
\(=\left(x-1\right)^2+\left(y+3\right)^2\)
4)
\(=x^2-2xy+y^2+x^2+10x+25\)
\(=\left(x-y\right)^2+\left(x+5\right)^2\)
5)
\(=a^2+2ab+b^2+4b^2+4b+1\)
\(=\left(a+b\right)^2+\left(2b+1\right)^2\)
1/ x2 - 4x + 5 + y2 + 2y
= ( x2 - 4x + 4 ) + ( y2 + 2y + 1 )
= ( x - 2 )2 + ( y + 1 )2
2/ 2a2 + 2ab - 2ax + x2 + b2
= ( a2 + 2ab + b2 ) + ( x2 - 2ax + a2 )
= ( a + b )2 + ( x - a )2
3/ x2 - 2x + y2 + 6y + 10
= ( x2 - 2x + 1 ) + ( y2 + 6y + 9 )
= ( x - 1 )2 + ( y + 3 )2
4/ 2x2 + y2 - 2xy + 10x + 25
= ( x2 - 2xy + y2 ) + ( x2 + 10x + 25 )
= ( x - y )2 + ( x + 5 )2
5/ a2 + 2ab + 5b2 + 4b + 1
= ( a2 + 2ab + b2 ) + ( 4b2 + 4b + 1 )
= ( a + b )2 + ( 2b + 1 )2
a) \(9x^2+6x+1=\left(3x+1\right)^2\)
b)\(x^2-x+\frac{1}{4}=\left(x-\frac{1}{2}\right)^2\)
c)\(x^2y^4-2xy^2+1=\left(xy^2-1\right)^2\)
d) \(x^2+\frac{2}{3}x+\frac{1}{9}=\left(x+\frac{1}{3}\right)^2\)
a) 9x2 + 6x + 1 = ( 3x + 1 )2
b) x2 - x + 1/4 = ( x - 1/2)2
c) x2 . y4 - 2xy2 + 1 = ( xy2 - 1 ) 2
d) x2 + 2/3x + 1/9 = (x+1/3)2
\(153^2+153.94+47^2\)
\(=153^2+2.153.47+47^2\)
\(=\left(153+47\right)^2\)
\(=200^2=40000\)
Mình sửa lại đề bài nhé
\(x^2+4y^2+2\left(3x+6y+2xy\right)+9\)
\(=x^2+4y^2+6x+12y+4xy+9\)
\(=\left(x^2+4xy+4y^2\right)+\left(6x+12y\right)+9\)
\(=\left(x+2y\right)^2+6\left(x+2y\right)+9\)
\(=\left(x+2y\right)^2+2.\left(x+2y\right).3+3^2\)
\(=\left(x+2y+3\right)^2\)
Chúc bạn học tốt.