Phân tích \
a, \(ax^2+cx^2-ay+ay^2-cy+cy^2^{ }\)
b,,\(ac^2-ad-bc^2cd+bd-c^3\)
K
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KT
22 tháng 7 2018
\(x^2+2xy+y^2-xz-yz\)
\(=\left(x+y\right)^2-z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y-z\right)\)
mk chỉnh lại đề
\(x^2-2xy+y^2-z^2+2zt+t^2\)
\(=\left(x-y\right)^2-\left(z-t\right)^2\)
\(=\left(x-y-z+t\right)\left(x-y+z-t\right)\)
mk chỉnh lại đề:
\(ax^2+cx^2-ay+ay^2-cy+cy^2\)
\(=x^2\left(a+c\right)-y\left(a+c\right)+y^2\left(a+c\right)\)
\(=\left(a+c\right)\left(x^2-y+y^2\right)\)
\(ax^2+ay^2-bx^2-by^2+b-a\)
\(=x^2\left(a-b\right)+y^2\left(a-b\right)-\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2+y^2-1\right)\)
\(ac^2-ad-bc^2+cd+bd-c^3\)
\(=a\left(c^2-d\right)-b\left(c^2-d\right)-c\left(c^2-d\right)\)
\(=\left(c^2-d\right)\left(a-b-c\right)\)
TA
25 tháng 7 2017
Bài 1 :
a ) \(x^2-6x-y^2+9=\left(x^2-6x+9\right)-y^2=\left(x-3\right)^2-y^2=\left(x-3+y\right)\left(x-3-y\right)\)
b) \(25-4x^2-4xy-y^2=5^2-\left(4x^2+4xy+y^2\right)=5^2-\left(2x+y\right)^2=\left(5+2x+y\right)\left(5-2x-y\right)\)
c) \(x^2+2xy+y^2-xz-yz=\left(x+y\right)^2-z.\left(x+y\right)=\left(x+y\right)\left(x+y-z\right)\)
d) \(x^2-4xy+4y^2-z^2+4tz-4t^2=\left(x^2-4xy+4y^2\right)-\left(z^2-4tz+4t^2\right)\)
\(=\left(x-2y\right)^2-\left(z-2t\right)^2=\left(x-2y+z-2t\right).\left(x-2y-z+2t\right)\)
BÀi 2 :
a) \(ax^2+cx^2-ay+ay^2-cy+cy^2=\left(ax^2+cx^2\right)-\left(ay+cy\right)+\left(ay^2+cy^2\right)\)
\(=x^2.\left(a+c\right)-y\left(a+c\right)+y^2.\left(a+c\right)=\left(a+c\right).\left(x^2-y+y^2\right)\)
b) \(ax^2+ay^2-bx^2-by^2+b-a=\left(ax^2-bx^2\right)+\left(ay^2-by^2\right)-\left(a-b\right)\)
\(=x^2.\left(a-b\right)+y^2.\left(a-b\right)-\left(a-b\right)=\left(a-b\right)\left(x^2+y^2-1\right)\)
c) \(ac^2-ad-bc^2+cd+bd-c^3=\left(ac^2-ad\right)+\left(cd+bd\right)-\left(bc^2+c^3\right)\)
\(=-a.\left(d-c^2\right)+d.\left(b+c\right)-c^2.\left(b+c\right)=\left(b+c\right).\left(d-c^2\right)-a\left(d-c^2\right)\)
\(=\left(b+c-a\right)\left(d-c^2\right)\)
BÀi 3 :
a) \(x.\left(x-5\right)-4x+20=0\) \(\Leftrightarrow x\left(x-5\right)-4\left(x-5\right)=0\) \(\Leftrightarrow\left(x-5\right)\left(x-4\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x-5=0\\x-4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=5\\x=4\end{cases}}}\)
b) \(x.\left(x+6\right)-7x-42=0\)\(\Leftrightarrow x.\left(x+6\right)-7.\left(x+6\right)=0\) \(\Leftrightarrow\left(x+6\right)\left(x-7\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x+6=0\\x-7=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=-6\\x=7\end{cases}}}\)
c) \(x^3-5x^2+x-5=0\) \(\Leftrightarrow x^2.\left(x-5\right)+\left(x-5\right)=0\) \(\Leftrightarrow\left(x-5\right)\left(x^2+1\right)\)
\(\Leftrightarrow\hept{\begin{cases}x^2+1=0\\x-5=0\end{cases}\Leftrightarrow\hept{\begin{cases}x^2=-1\left(KTM\right)\\x=5\end{cases}}}\)
d) \(x^4-2x^3+10x^2-20x=0\) \(\Leftrightarrow x.\left(x^3-2x^2+10x-20\right)=0\)\(\Leftrightarrow x.\left[x^2.\left(x-2\right)+10.\left(x-2\right)\right]=0\) \(\Leftrightarrow x.\left(x-2\right)\left(x^2+10=0\right)\)
\(\Leftrightarrow\hept{\begin{cases}x=0\\x-2=0\\x^2+10=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=0\\x=2\\x^2=-10\left(KTM\right)\end{cases}}}\)
D
1
17 tháng 1 2018
ĐẶT NHÂN TỬ CHUNG NHA!
1) ab - ac + ad = a( b- c +d )
2) ax - bx - cx + dx = x( a-b-c+d)
3) a.( b + c ) - d . ( b + c )= (b+c)(a-d)
4) ac - ad + bc - bd = a( c-d) + b( c-d) = (a+b)(c-d)
5) ax + by + bx + ay= a( x+y) + b( x+y) = (a+b)(x+y)
TQ
2
12 tháng 10 2021
\(b,=\left(x+y\right)-x\left(x+y\right)=\left(1-x\right)\left(x+y\right)\\ c,=x\left(x-y\right)-7\left(x-y\right)=\left(x-7\right)\left(x-y\right)\\ d,=x^2\left(a+c\right)-y\left(a+c\right)+y^2\left(a+c\right)\\ =\left(x^2-y+y^2\right)\left(a+c\right)\)
Câu a sai đề, không phân tích được
12 tháng 10 2021
a: \(xy+xz-5x-5y=\left(x+y\right)\left(z-5\right)\)
b: \(x+y-x^2-xy=\left(x+y\right)\left(1-x\right)\)
c: \(x^2-xy-7x+7y=\left(x-y\right)\left(x-7\right)\)
20 tháng 12 2017
1) ab + ac = a(b + c)
2) ab - ac + ad = a(b - c + d)
3) ax - bx - cx + dx = x(a - b - c + d)
4) a(b + c) - d(b + c) = (b + c)(a - d)
5) ac - ad + bc - bd = a(c - d) + b(c - d) = (c - d)(a + b)
6) ax + by + bx + ay = (ax + ay) + (bx + by) = a(x + y) + b(x + y) = (x + y)(a + b)
HB
25 tháng 1 2018
ab + ac = a ( b + c )
ab - ac + ad = a ( b - c + d )
ax - bx - cx + dx = x ( a - b - c + d )
30 tháng 1 2017
1/ab+ac=a(b+c)
2/ab-ac+ad=a(b-c)+ad=a(b-c+d)
3/ax-bx-cx+dx=x(a-b-c)+xd=x(a-b-c+d)
4/a(b+c)-d(b+c)=(ab+ac)-(bd+cd)=b(a+d)-c(a+d)=a+d(b+c)
5/ac-ad+bc-bd=a(c-d)+b(c-d)=c-d(a+b)
6/ax+by+bx+ay=a(x+y)+b(x+y)=x+y(a+b)
24 tháng 1 2017
1?
a(b+c)
a(b-c+d)
x(a-b-c+d)
(b+c)(a-d)
(c-d)(a+b)
(x+-y)(a+b)
W
27 tháng 2 2020
1/ ab+ ac
=a(b+c)
2/ ab - ac + ad
=a(b-c+d)
3/ ax - bx - cx + dx
=x(a-b-c+d)
4/ a(b + c) - d(b + c)
=(a-d)(b+c)
5/ ac - ad + bc - bd
=a(c-d)+b(c-d)
=(a+b)(c-d)
6/ ax + by + bx + ay
=x(a+b)+y(b+a)
=(x+y)(b+a)
27 tháng 2 2020
A) ab + ac=a.(b+c)
B)ab - ac + ad=a.(b-c+d)
C) ã-bx-cx+dx=x.(a-b-c+d)
D)a(b+c) - d(b+c)=(b+c).(a-d)
E) ac-ad+bc-bd=a.(c-d)+b.(c-d)=(c-d).(a+b)
G) ax+by+bx+ay=x.(a+b)+y.(b+a)=(a+b).((x.y)
a)\(\left(x-2y-z+2t\right)\left(x-2y+z-2t\right)\)
\(=\left(x-2y\right)^2-\left(z-2t\right)^2\)
\(=x^2-4xy+4y^2-z^2+4zt-4t^2\)
b)\(ax^2+ay^2-bx^2-by^2+b-a\)
\(=a\left(x^2+y\right)-b\left(x^2+y^2\right)-\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2+y^2\right)-\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2+y^2-1\right)\)