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\(x^2+6x+9=\left(x+3\right)^2\)
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\(x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)^2\)
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\(x^3+12x^2+48x+64=\left(x+4\right)^3\)
1) \(\dfrac{\left(x+5\right)^2+\left(x-5\right)^2}{x^2+25}\)
\(=\dfrac{x^2+10x+25+x^2-10x+25}{x^2+25}\)
\(=\dfrac{2x^2+50}{x^2+25}\)
\(=\dfrac{2\left(x^2+25\right)}{x^2+25}=2\)
2) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
\(=x^3+3^3-54-x^3\)
\(=27-54=-27\)
3) \(\left(2x+y\right)^2-\left(y+3x\right)^2\)
\(=4x^2+4xy+y^2-y^2-6xy-9x^2\)
\(=-5x^2-2xy\)
4) \(\left(2x+1\right)^3-\left(2x-1\right)^3-24x^2\)
\(=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-24x^2\)
\(=2\)
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
1)\(25x^2y^4+30xy^2z+9z^2=\left(5xy^2+3z\right)^2\)
\(\dfrac{16}{9}x^2+4xyz^2+\dfrac{9}{4}y^2z^4=\left(\dfrac{4}{3}x+\dfrac{3}{2}yz^2\right)^2\)
2)
a)\(\dfrac{9}{25}x^2+\dfrac{12}{35}xy+\dfrac{4}{49}y^2=\left(\dfrac{3}{5}x+\dfrac{2}{7}y\right)^2=\left(\dfrac{3}{5}.5+\dfrac{2}{7}.\left(-7\right)\right)^2=\left(3-2\right)^2=1\)b)\(\dfrac{25}{16}u^4v^2+\dfrac{1}{5}u^2v^3+\dfrac{4}{625}v^4\)
\(=\left(\dfrac{5}{4}u^2v+\dfrac{2}{25}v^2\right)^2=\left(\dfrac{5}{4}.\dfrac{4}{25}.\left(-5\right)+\dfrac{2}{25}.\left(-5\right)^2\right)^2\)
\(=\left(-1+2\right)^2=1\)
a) \(9x^2+6x+1=\left(3x\right)^2+2.3x.1+1^2=\left(3x+1\right)^2\)
b) \(x^2-x+\dfrac{1}{4}=x^2-2.\dfrac{1}{2}x+\left(\dfrac{1}{2}\right)^2=\left(x-0,5\right)^2\)
c) \(x^2y^4-2xy^2+1=\left(xy^2\right)^2-2.xy^2.1+1^2=\left(xy^2-1\right)^2\)
d) \(x^2+\dfrac{2}{3}x+\dfrac{1}{9}=x^2+2.x.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2=\left(x+\dfrac{1}{3}\right)^2\)
a) \(9x^2+6x+1\)
\(=\left(3x\right)^2+2.3x.1+1^2\)
\(=\left(3x+1\right)^2\)
a) x2 +4x+4 = ( x + 2 )2
b) 16x2 - 8xy + y2 = ( 4x - y )2
c)9a2 +16b2 - 24ab = ( 3a - 4y ) 2
d) x2 - x + \(\dfrac{1}{4}\)= ( x - \(\dfrac{1}{2}\))2
e) y2 + \(\dfrac{1}{2}y\) + \(\dfrac{1}{16}\) = ( y + \(\dfrac{1}{4}\))2
\(25x^2y^4+30xy^2z+9z^2=\left(5xy^2\right)^2+2.5xy^2.3z+\left(3z\right)^2=\left(5xy^2+3z\right)^2\)
\(\frac{16}{9}x^2+4xyz^2+\frac{9}{4}y^2z^4=\left(\frac{4}{3}x\right)^2+2.\frac{4}{3}x.\frac{3}{2}yz^2+\left(\frac{3}{2}yz^2\right)^2=\left(\frac{4}{3}x+\frac{3}{2}yz^2\right)^2\)
\(\frac{9}{25}x^2+\frac{12}{35}xy+\frac{4}{49}y^2=\left(\frac{3}{5}x\right)^2+2.\frac{3}{5}x.\frac{2}{7}y+\left(\frac{2}{7}y\right)^2=\left(\frac{3}{5}x+\frac{2}{7}y\right)^2\)( tự thay vào tính nhé )
\(\frac{25}{16}u^4y^2+\frac{1}{5}u^2+y^3+\frac{4}{625}y^4=\left(\frac{5}{4}u^2y\right)^2+2.\frac{5}{4}u^2y.\frac{2}{25}.y^2+\left(\frac{2}{25}y^2\right)^2=\left(\frac{5}{4}u^2y+\frac{2}{25}y^2\right)^2\)( tự thay vào tính nhé )
Tham khảo nhé~
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
bài 1:
a) x2 + 10x + 26 + y2 + 2y
= (x2 + 10x + 25) + (y2 + 2y + 1)
= (x + 5)2 + (y + 1)2
b) z2 - 6z + 5 - t2 - 4t
= (z - 3)2 - (t + 2)2
c) x2 - 2xy + 2y2 + 2y + 1
= (x2 - 2xy + y2) + (y2 + 2y + 1)
= (x - y)2 + (y + 1)2
d) 4x2 - 12x - y2 + 2y + 1
= (4x2 - 12x ) - (y2 + 2y + 1)
= ......................................
ok mk nhé!! 4545454654654765765767587876968345232513546546575675767867876876877687975675
