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a) -25x6 - y8 + 10x3y4 = -25x6 + 10x3y4 - y8
= - ( 25x6 - 10x3y4 + y8 )
= - [ ( 5x3 )2 - 2 . 5x3y4 + ( y4 )2 ]
= - ( 5x3 - y4 )2
b) \(\dfrac{1}{4}\)x2 - 5xy + 25y2 = (\(\dfrac{1}{2}\)x)2 - 2 . \(\dfrac{1}{2}\) x . 5y + ( 5y )2
= (\(\dfrac{1}{2}\) x - 5y )2
c) ( x - 5 )2 - 16 = ( x - 5 )2 - 42
= ( x - 5 - 4 ) . ( x - 5 + 4 )
= ( x - 9 ) . ( x - 1 )
d) 25 - ( 3 - x )2 = 52 - ( 3 - x )2
= ( 5 - 3 + x ) . ( 5 + 3 - x )
= ( x + 2 ) . ( 8 - x )
a) \(4x^2-12x+9=\left(2x\right)^2-2.2x.3+3^2=\left(2x-3\right)^2\)
b) \(4x^2+4x+1=\left(2x\right)^2+2.2x.1+1^2=\left(2x+1\right)^2\)
c) \(1+12x+36x^2=1^2+2.6x.1+\left(6x\right)^2=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2=\left(3x\right)^2-2.3x.4y+\left(4y\right)^2=\left(3x-4y\right)^2\)
f) \(-x^2+10x-25=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)
g) \(-16a^4b^6-24a^5b^5-9a^6b^4=-\left(16a^4b^6+24a^5b^5+9a^6b^4\right)\)
\(=-\left[\left(4a^2b^3\right)^2+2.4a^2b^3.3a^3b^2+\left(3a^3b^2\right)^2\right]\)
\(=-\left(4a^2b^3+3a^3b^2\right)^2\)
h) \(25x^2-20xy+4y^2=\left(5x\right)^2-2.5x.2y+\left(2y\right)^2\) \(=\left(5x-2y\right)^2\)
i) \(25x^4-10x^2y+y^2=\left(5x^2\right)^2-2.5x^2.y+y^2=\left(5x^2-y\right)^2\)
Bài 1:
a) \(\left(n+2\right)^2-\left(n-2\right)^2=n^2+4n+4-\left(n^2-4n+4\right)=8n\) \(⋮\)\(8\) (đpcm)
b) \(\left(n+7\right)^2-\left(n-5\right)^2=n^2+14n+49-\left(n^2-10n+25\right)=24n-24\)\(⋮\)\(24\) (đpcm)
Bài 2:
mk biến đổi về pt tích sau đó bạn giải nốt nhé
a) \(\left(x-4\right)^2-36=0\)
<=> \(\left(x-4-6\right)\left(x-4+6\right)=0\)
<=> \(\left(x-10\right)\left(x+2\right)=0\)
................
b) \(4x^2-12x=-9\)
<=> \(4x^2-12x+9=0\)
<=> \(\left(2x-3\right)^2=0\)
..............
c) \(\left(x+8\right)^2=121\)
<=> \(\left(x+8\right)^2-121=0\)
<=> \(\left(x+8+11\right)\left(x+8-11\right)=0\)
<=> \(\left(x+19\right)\left(x-3\right)=0\)
...................
Bài 1:
a) 25\(x^2\) - 0,09
= \(\left(5x\right)^2-0,3^2\)
= (5x - 0,3) (5x +0,3)
Bài 5:
a: \(=\left(2x-3\right)^2\)
b: \(=\left(2x+1\right)^2\)
c: \(=\left(6x+1\right)^2\)
d: \(=\left(3x-4y\right)^2\)
e: \(=\left(\dfrac{1}{2}x-2y\right)^2\)
f: \(=-\left(x-5\right)^2\)
Bài 8:
b. 1+8x6y3 = 13+23(x2)3y3 = 13+(2x2y)3
= (1+2x2y)(1-2x2y+4x4y2)
e. 27x3+\(\dfrac{y^3}{8}\)\(=\left(3x\right)^3+\left(\dfrac{y}{2}\right)^3\)
= (3x+\(\dfrac{y}{2}\))(9x2-\(\dfrac{3xy}{2}\)+\(\dfrac{y^2}{4}\))
Bài 9:
c. 1- 9x +27x2 -27x3 = 13-3.12.3x+3.(3x)2-(3x)3
= (1-3x)3
d. x3+\(\dfrac{3}{2}x^2\)+\(\dfrac{3}{4}x+\dfrac{1}{8}\) = x3+\(3x^2.\dfrac{1}{2}\)+\(3x.\dfrac{1}{4}+\left(\dfrac{1}{2}\right)^3\)
= (x+\(\dfrac{1}{2}\))3
f. x2 - 2xy +y2 -4m2 +4m.n - n2 = (x2 - 2xy +y2)-((2m)2 -2.2m.n + n2)
= (x-y)2-(2m-n)2 = (x-y-2m+n)(x-y+2m-n)
a) Ta có: \(\left(4x^2-12x+9\right)-1\)
\(=\left(2x-3\right)^2-1^2\)
\(=\left(2x-3-1\right)\left(2x-3+1\right)\)
\(=\left(2x-4\right)\left(2x-2\right)\)
\(=4\left(x-2\right)\left(x-1\right)\)
b) Ta có: \(\left(\frac{x^2}{4}+2xy+4y^2\right)-25\)
\(=\left[\left(\frac{x}{2}\right)^2+2\cdot\frac{x}{2}\cdot2y+\left(2y\right)^2\right]-5^2\)
\(=\left(\frac{x}{2}+2y\right)^2-5^2\)
\(=\left(\frac{x}{2}+2y-5\right)\left(\frac{x}{2}+2y+5\right)\)
c) Ta có: \(1+12x+35x^2\)
\(=35x^2+12x+1\)
\(=35x^2+5x+7x+1\)
\(=5x\left(7x+1\right)+\left(7x+1\right)\)
\(=\left(7x+1\right)\left(5x+1\right)\)
d) Ta có: \(9x^2-24xy+15y^2\)
\(=9x^2-9xy-15xy+15y^2\)
\(=9x\left(x-y\right)-15y\left(x-y\right)\)
\(=\left(x-y\right)\left(9x-15y\right)\)
\(=3\left(x-y\right)\left(3x-5y\right)\)
e) Ta có: \(25x^2-20xy+3y^2\)
\(=25x^2-15xy-5xy+3y^2\)
\(=5x\left(5x-3y\right)-y\left(5x-3y\right)\)
\(=\left(5x-3y\right)\left(5x-y\right)\)
f) Ta có: \(24x^4-10x^2y+y^2\)
\(=24x^4-4x^2y-6x^2y+y^2\)
\(=4x^2\left(6x^2-y\right)-y\left(6x^2-y\right)\)
\(=\left(6x^2-y\right)\left(4x^2-y\right)\)
bai 3
a) 36-12x+x2
= x2-12x+36
=(x-6)2
b) 4x2+12x+9
=(2x+3)2
c) -25x6-y8+10x3y4
=-(25x6+y8-10x3y4)
=-(5x3)2+(y4)2-10x3y4
=-(5x3)2-2.5x3y4+(y4)
=-(5x3-y4)2
d) \(\dfrac{1}{4}\) x2-5xy+25y2
=(\(\dfrac{1}{2}\) x-5y)2
Bài3:
Bạn =kia làm r nhé
Bài4:
\(a,75^2-25^2\\ =\left(75-25\right)\left(75+25\right)\\ =50.100=5000\\ b,53^2-47^2\\ =\left(53-47\right)\left(53+47\right)\\ =6.100=600\\ c,31,8^2-2.31,8.21,8+21,8^2\\ =\left(31,8-21,8\right)^2\\ =10^2=100\\ d,58,2+2.58,2.41,8+41,8^2\\ =\left(58,2+41,8\right)^2\\ =100^2=1000\)