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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`
A, \(\frac{9}{4}x^2+3x+4\)
= \(\left(\frac{3}{2}x^2\right)+2\cdot\frac{3}{2}x\cdot2+2^2\)
= \(\left(\frac{3}{2}x+2\right)^2\)
(2x+3y)2+2(2x+3y)+1=[(2x+3y)+1)]2=(2x+3y+1)2
9x2-6x+1=(3x)2-2.3x+12=(3x-1)2
a) x2 + 2x + 1 = x2 + 2.x.1+ 12 = ( x + 1)2
b) 9x2 + y2 + 6xy = (3x)2 + 2.3.x.y + y2 = (3x + y)2
c) 25a2 + 4b2 – 20ab = (5a)2 – 2.5.a.2b. + (2b)2 = (5a – 2b)2
Hoặc 25a2 + 4b2 – 20ab = (2b)2 – 2.2b.5a. + (5a)2 = (2b – 5a)2
d) x2 – x + \(\dfrac{1}{4}\) = x2 – 2.x. \(\dfrac{1}{2}\) + ( \(\dfrac{1}{2}\))22 = ( x - \(\dfrac{1}{2}\) )2
Hoặc x2 – x + \(\dfrac{1}{4}\) = \(\dfrac{1}{4}\) - x + x2 = (\(\dfrac{1}{2}\))2 – 2. \(\dfrac{1}{2}\).x + x2 = (\(\dfrac{1}{2}\) - x)2
a) x2 + 2x + 1 = x2+ 2 . x . 1 + 12
= (x + 1)2
b) 9x2 + y2+ 6xy = (3x)2 + 2 . 3 . x . y + y2 = (3x + y)2
c) 25a2 + 4b2– 20ab = (5a)2 – 2 . 5a . 2b + (2b)2 = (5a – 2b)2
Hoặc 25a2 + 4b2 – 20ab = (2b)2 – 2 . 2b . 5a + (5a)2 = (2b – 5a)2
d) x2 – x + 1414 = x2 – 2 . x . 1212 + (12)2(12)2= (x−12)2(x−12)2
Hoặc x2 – x + 1414 = 1414 - x + x2 = (12)2(12)2 - 2 . 1212 . x + x2 = (12−x)2
a) 9x2 – 6x + 1 = (3x)2 – 2 . 3x . 1 + 12 = (3x – 1)2
Hoặc 9x2 – 6x + 1 = 1 – 6x + 9x2 = (1 – 3x)2
b) (2x + 3y) = (2x + 3y)2 + 2 . (2x + 3y) . 1 + 12
= [(2x + 3y) + 1]2
= (2x + 3y + 1)2
Đề bài tương tự. Chẳng hạn:
1 + 2(x + 2y) + (x + 2y)2
4x2 – 12x + 9…
a) \(9x^2-6x+1=\left(3x\right)^2-2.3x.1+1^2=\left(3x-1\right)^2\)
b) \(\left(2x+3y\right)^2+2\left(2x+3y\right)+1=\left[\left(2x+3y\right)+1\right]^2=\left(2x+3y+1\right)^2\)
a) =(3x)2-2.3x+1 =(3x-1)2
b) tương tự ta có gái trị biểu thức =(2x+3y+1)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.
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