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a) \(9\left(a+b\right)^2-4\left(a-2b\right)^2\)
\(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)
\(=\left(3a+3b-2a+4b\right)\left(3a+3b+2a-4b\right)\)
\(=\left(a+7b\right)\left(5a-b\right)\)
b) \(9x^6-12x^7+4x^8\)
\(=x^6\left(9-12x+4x^2\right)\)
\(=x^6\left(2x-3\right)^2\)
c) \(8x^6-27y^3\)
\(=\left(2x^2\right)^3-\left(3y\right)^3\)
\(=\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
d) \(\frac{1}{64}x^6-125y^3\)
\(=\left(\frac{1}{4}x^2\right)^3-\left(5y\right)^3\)
\(=\left(\frac{1}{4}x^2-5y\right)\left(\frac{1}{16}x^4+\frac{5}{6}xy+25y^2\right)\)
a) \(-5x^2+16x-3=-5x^2+15x+x-3=-5x\left(x-3\right)+x-3=\left(x-3\right)\left(1-5x\right).\)
b) \(x^4+64=x^4+16x^2+64-16x^2=\left(x^2+8\right)^2-\left(4x\right)^2=\left(x^2+4x+8\right)\left(x^2-4x+8\right).\)
c) \(64x^2+4y^4=4\left(16x^2+y^4\right)\)
d) \(x^5+x-1\)đa thức này có nghiệm vô tỷ. Mik ko phân tích được.
a/ x^3-6x^2+12x-8
=(x-2)^3
b/x^2+5x+4
=x^2+x+4x+4
=x(x+1)+4(x+1)
=(x+1)(x+4)
c/ 16^2-9(x+1)^2=0
<=> (4x-3x-3)(4x+3x+3)=0
<=>x-3=0 hay 7x+3=0
<=> x=3 hay x=-3/7
d/ x^3-2x^2-x+2
=x^2(x-2)-(x-2)
=(x-2)(x^2-1)
=(x-2)(x-1)(x+1)
e/x^2+y^2-2xy-x+y
=(x-y)^2-(x-y)
f/x^3+y^3+3y^2+3y+1
=x^3+(y+1)^3
=(x+y+1)[x^2-xy-x+(y+1)^2]
=(x+y+1)(x^2-xy-x+y^2+2y+1)
b. x2+2.5/2x+(5/2)2-(5/2)2+4
= (x+5/2)2-25/4+4
=(x+5/2)2-(3/2)2
= x+ 5/2 -3/2 ) . (x+5/2-3/2)
= (x+1 ) (x+2)
c.
(4x)2- [3(x+1)]2 =0
[4x-3(x+1)] [4x+3(x+1)] =0
(x-3) (7x+3) =0
<=> x-3 =0 => x = 3
7x+3=0 => x= -3/7
d. x3-2x2-x+2
= (x3-2x2) - (x+2)
= x2 (x-2) - (x-2)
= (x-2) (x2-1)
CHÚC BẠN HỌC TỐT
* Tớ còn a, e, và f sorry nó k dễ để suy nghĩ trong thơi gian ngắn được nên tớ bỏ !! Ahihihih
a) \(x^2+12x+35\)
\(=x^2+5x+7x+35\)
\(=\left(x^2+5x\right)+\left(7x+35\right)\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
b)\(x^2-x-56\)
\(=x^2+7x-8x-56\)
\(=\left(x^2+7x\right)-\left(8x+56\right)\)
\(=x\left(x+7\right)-8\left(x+7\right)\)
\(=\left(x+7\right)\left(x-8\right)\)
c)\(5x^2-x-4\)
\(=5x^2-5x+4x-4\)
\(=\left(5x^2-5x\right)+\left(4x-4\right)\)
\(=5x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
TL:
a)\(x^2+5x+7x+35\)
=\(x\left(x+5\right)+7\left(x+5\right)\)
=\(\left(x+7\right)\left(x+5\right)\)
b) \(x^2-x-56\)
=\(x^2+7x-8x-56\)
=\(x\left(x+7\right)-8\left(x+7\right)\)
=\(\left(x-8\right)\left(x+7\right)\)
d)\(4x^4+1=\left(2x^2\right)^2+4x^2+1-4x^2\)
=\(\left(2x^2+1\right)^2-4x^2\)
=\(\left(2x^2+1+4x\right)\left(2x^2+1-4x\right)\)
.......................(tự lm)
hc tốt
a)6x2-12x=6x(x-2)
b)x2-12x+36=(x-6)2
c)8xy-16x2-y2=-(4x-y)2
d)125x3+1/64=(5x+1/4)(25x2-5/4x+1/16)
e)1/64x2+1/64=1/64(x2+1)
a, 6x^2 - 12x = 6x ( x-2)
b, x^2 - 12x + 36 = x^2 - 2.x.6 + 36 = ( x -6)^2
c, 8xy - 16x^2 - y^2 = - [ 16x^2 - 8xy + y^2) = - (4x - y)^2
d, 125y^3 + 1/64 = ( 5y + 1/4)(25y^2 - 5/4y + 1/16)
e, 1/64 x^2 + 1/64 = 1/64( x^2+1)