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a)
áp dụng hằng đẳng thức hiệu 2 bình phương
\(\left(x-2\right)^2-\left(4\right)^2=\left(x-2-4\right)\left(x-2+4\right)=\left(x-6\right)\left(x-2\right)\)
b)
áp dụng HDT : bình phương của 1 hiệu
\(\left(x-2y\right)^2-2.2.\left(x-2y\right)+2^2=\left(x-2y-2\right)^2=\left(x-2y-2\right)\left(x-2y-2\right)\)
c)
áp dụng HDT : bình phương của 1 hiệu
\(\left(a^2+1\right)^2-2.3.\left(a^2+1\right)+3^2=\left(a^2+1-3\right)^2=\left(a^2-2\right)^2=\left(a^2-2\right)\left(a^2-2\right)\)
d) áp dụng HDT : bình phương của 1 tồng
\(\left(x+y\right)^2+2.\frac{1}{2}.\left(x+y\right).x+\left(\frac{1}{2}x\right)^2=\left(x+y+\frac{1}{2}x\right)^2=\left(\frac{3}{2}x+y\right)\left(\frac{3}{2}x+y\right)\)
Chúc bạn học tốt nha!!!
T I C K ủng hộ nha
Bài 2;
\(a)x^4-16x=0\Rightarrow x^4=16x\Leftrightarrow x^3=16\Leftrightarrow x=\sqrt[3]{16}\)
\(c)4x^2-\frac{1}{4}=0\Leftrightarrow4x^2=\frac{1}{4}\Leftrightarrow x^2=\frac{1}{16}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{4}\\x=-\frac{1}{4}\end{cases}}\)
1)\(21x^2y-12xy^2=xy.\left(21x-12y\right)\)
2)\(x^3+x^2-2x=x.\left(x^2+x-2\right)\)
3)\(3x.\left(x-1\right)+7x^2\left(x-1\right)=\left(x-1\right).\left(3x+7x^2\right)=x.\left(x-1\right)\left(3+7x\right)\)
15)\(\left(2a+3\right)^2-\left(2a+1\right)^2=\left(2a+3-2a-1\right)\left(2a+3+2a+1\right)=2.\left(4a+4\right)=8\left(a+1\right)\)
14) \(-4y^2+4y-1=-\left[\left(2y\right)^2-2.2y.1+1^2\right]=-\left(2y-1\right)^2\)
13) \(x^6+1=\left(x^2\right)^3+1=\left(x^2+1\right)\left(x^4-x^2+1\right)\)
12) \(\left(x+1\right)^2-\left(y+6\right)^2=\left(x+1-y-6\right)\left(x+1+y+6\right)=\left(x-y-5\right)\left(x+y+7\right)\)
4) \(3x\left(x-a\right)+4a\left(a-x\right)=3x.\left(x-a\right)-4a\left(x-a\right)=\left(x-a\right)\left(3x-4a\right)\)
Sao nhiều thế!
a) 5xy ( x - y ) - 2x + 2y
= 5xy ( x - y ) - 2 ( x - y )
= ( x - y ) ( 5xy - 2 )
b) 6x-2y-x(y-3x)
= 2 ( y - 3x ) - x ( y - 3x )
= ( y - 3x ( ( 2 - x )
c) x2 + 4x - xy-4y
= x ( x + 4 ) - y ( x + 4 )
( x + 4 ) ( x - y )
d) 3xy + 2z - 6y - xz
= ( 3xy - 6y ) + ( 2z - xz )
= 3y ( x - 2 ) + z ( x - 2 )
= ( x - 2 ) ( 3y + z )
a,5xy(x-y)-2x+2y=5xy(x-y)-2(x-y)=(x-y)(5xy-2)
b,6x-2y-x(y-3x)=-2(y-3x)-x(y-3x)=(y-3x)(-2-x)
c,x^2+4x-xy-4y=x(x+4)-y(x+4)=(x+4)(x-y)
d,3xy+2z-6y-xz=(3xy-6y)+(2z-xz)=3y(x-2)+z(2-x)=3y(x-2)-z(x-2)=(x-2)(3y-z)
11)
a,4-9x^2=0
(2-3x)(2+3x)=0
2-3x=0=>x=2/3 hoặc 2+3x=0=>x=-2/3
b,x^2 +x+1/4=0
(x+1/2)^2 =0
x+1/2=0
x=-1/2
c,2x(x-3)+(x-3)=0
(x-3)(2x+1)=0
x-3=0=>x=3 hoặc 2x+1=0=>x=-1/2
d,3x(x-4)-x+4=0
3x(x-4)-(x-4)=0
(x-4)(3x-1)=0
x-4=0=>x=4 hoặc 3x-1=0=>x=1/3
e,x^3-1/9x=0
x(x^2-1/9)=0
x(x+1/3)(x-1/3)=0
x=0 hoặc x+1/3=0=>x=-1/3 hoặc x-1/3=0=>x=1/3
f,(3x-y)^2-(x-y)^2 =0
(3x-y-x+y)(3x-y+x-y)=0
2x(4x-2y)=0
4x(2x-y)=0
x=0hoặc 2x-y=0=>x=y/2
1a/ z2 - 6z + 5 - t2 - 4t = z2 - 2 . 3z + 32 - 4 - t2 - 4t = (z2 - 2 . 3z + 32) - (22 + 2 . 2t + t2) = (z - 3)2 - (2 + t)2
b/ x2 - 2xy + 2y2 + 2y2 + 1 = x2 - 2xy + y2 + y2 + 2y + 1 = (x2 - 2xy + y2) + (y2 + 2y + 1) = (x - y)2 + (y + 1)2
c/ 4x2 - 12x - y2 + 2y + 8 = (2x)2 - 12x - y2 + 2y + 32 - 1 = [ (2x)2 - 2 . 3 . 2x + 32 ] - (y2 - 2y + 1) = (2x - 3)2 - (y - 1)2
2a/ (x + y + 4)(x + y - 4) = x2 + xy - 4x + xy + y2 - 4y + 4x + 4y + 16 = x2 + (xy + xy) + (-4x + 4x) + (-4y + 4y) + y2 + 16
= x2 + 2xy + y2 + 42 = (x + y)2 + 42
b/ (x - y + 6)(x + y - 6) = x2 + xy - 6x - xy - y2 + 6y + 6x + 6y - 36 = x2 + (xy - xy) + (-6x + 6x) + (6y + 6y) - y2 - 36
= x2 - y2 + 12y - 62 = x2 - (y2 - 12y + 62) = x2 - (y2 - 2 . 6y + 62) = x2 - (y - 6)2
c/ (y + 2z - 3)(y - 2z - 3) = y2 -2yz - 3y + 2yz - 4z2 - 6z - 3y + 6z + 9 = y2 + (-2yz + 2yz) + (-3y - 3y) + (-6z + 6z) - 4z2 + 9
= y2 - 6y - 4z2 + 9 = (y2 - 6y + 9) - 4z2 = (y - 3)2 - (2z)2
d/ (x + 2y + 3z)(2y + 3z - x) = 2xy + 3xz - x2 + 4y2 + 6yz - 2xy + 6yz + 9z2 - 3xz = (2xy - 2xy) + (3xz - 3xz) - x2 + (6yz + 6yz) + 9z2 + 4y2
= -x2 + 4y2 + 12yz + 9z2 = (4y2 + 12yz + 9z2) - x2 = [ (2y)2 + 2 . 2 . 3yz + (3z)2 ] - x2 = (2y + 3z)2 - x2
\(\left(x+2y\right)^2-16=\left(x+2y-4\right)\left(x+2y+4\right)\)
\(\left(x-2y\right)^2-4\left(x-2y\right)+4=\left(x-2y-2\right)^2\)
\(\left(a^2+1\right)^2-6\left(a^2+1\right)+9=\left(a^2+1-3\right)^2=\left(a^2-2\right)^2\)
\(\left(x+y\right)^2+\left(x+y\right)x+\frac{1}{4}x^2=\left(x+y+\frac{1}{2}x\right)^2=\left(\frac{3}{2}x+y\right)^2\)
\(16x^4-9x^2=x^2\left(16x^2-9\right)=x^2\left(4x-4\right)\left(4x+3\right)\)
\(a^2-b^4=\left(a-b^2\right)\left(a+b^2\right)\)
(x + 2y)2 - 16
= (x + 2y)2 - 42
= (x + 2y - 4).(x + 2y + 4)
(x - 2y)2 - 4.(x - 2y) + 4
= (x - 2y)2 - 2.(x - 2y).2 + 22
= (x - 2y - 2)2
(a2 + 1)2 - 6.(a2 + 1) + 9
= (a2 + 1)2 - 2.(a2 + 1).3 + 32
= (a2 + 1 - 3)2
= (a2 - 2)2
(x + y)2 + (x + y).x + 1/4.x2
= (x + y)2 + 2.(x + y).1/2.x + (1/2.x)2
= (x + y + 1/2.x)2
= (3/2.x + y)2
16x4 - 9x2
= (4x2)2 - (3x)2
= (4x2 - 3x).(4x2 + 3x)
a2 - b4
= a2 - (b2)2
= (a - b2).(a + b2)