Phân tích các đa thức sau thành nhân :
a) ( 3x - 1)² - 16
b) ( 3x + 1)² - 4( x - 2)²
c) ( ax + by) ² - (ay + bx) ²
d) ( 4x² - 3x - 18 )² - ( 4x² + 3x )²
e) -4x² + 12xy - 9y² +25
g) x³ + 6x² + 12x + 8
h) x³ + 3/2x² + 3/4x + 1/8
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Phân tích các đa thức sau thành nhân tử:
a) (3x-1)^2 -16
b) (5x-4)^2 49x^2
c) (2x +5)^2 -(x-9)^2
d) (3x+1)^2 - 4(x-2)^2
e) 9(2x+3)^2 -4(x+1)^2
f)4b^2c^2 -(b^2+c^2-a^2)^2
g) (ax+by)^2 -(ay+bx)^2
h) (a^2+b^2-5)^2 -49ab+2)^2
i) (4x^2-3x-18)^2 -(4x^2 +3x)^2
k) 9(x+y-1)^2 4(2x+3y+1)^2
l) -4x^2 +12xy -9y^2+25
m) x^2 -2xy +y^2 -4m^2+4mn-n^2
a)\(\left(3x-1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\)
\(=\left(3x-17\right)\left(3x+15\right)\)
c)\(\left(2x+5\right)^2-\left(x-9\right)^2=\left(2x+5+x-9\right)\left(2x+5-x+9\right)\)
\(=\left(x-4\right)\left(x+14\right)\)
Aps dungj t/c a2 - b2 = ( a-b)(a+b)
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Phân tích các đa thức sau thành nhân tử:
a) -16a^4b^6 - 24a^5b^5 - 9a^9b^4
b) ( 3x - 1)^2 - 16
c) ( 3x + 1)^2 - 4( x - 2 )^2
d) ( ax + by) ^2 - ( ay + bx )^2
e) ( 4x^2 - 3x - 18)^2 - ( 4x^2 + 3x )^2
g) 8x^3 - 64
h) 8x^3 - 27
i) x^3 + 6x^2 + 12x + 8
k) x^3 + 3/2x^2 + 3/4x + 1/8
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Phân tích đa thức thành nhân tử
a) (4x^2 - 3x - 18)^2 - (4x^2 + 3x)^2
b) 9(x + y - 1)^2 - 4(2x + 3y +1)^2
c) -4x^2 + 12xy - 9y^2 + 25
d) x^2 - 2xy + y^2 - 4m^2 + 4mn - n^2
a) Ta có: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)
\(=\left(-6x-18\right)\left(8x^2-18\right)\)
\(=-6\left(x+3\right)\cdot2\left(4x^2-9\right)\)
\(=-12\left(x+3\right)\left(2x-3\right)\left(2x+3\right)\)
b) Ta có: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)
\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)
\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)
\(=-\left(x+3y+5\right)\left(7x+9y-1\right)\)
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c) Ta có: \(-4x^2+12xy-9y^2+25\)
\(=-\left(4x^2-12xy+9y^2-25\right)\)
\(=-\left[\left(2x-3y\right)^2-25\right]\)
\(=-\left(2x-3y-5\right)\left(2x-3y+5\right)\)
d) Ta có: \(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x^2-2xy+y^2\right)-\left(4m^2-4mn+n^2\right)\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)
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a) (4x2-3x-18)2-(4x2+3x)2
=(4x2-3x-18-4x2-3x)(4x2-3x-18+4x2+3x)
=(-6x-18)(8x2-18)
=-48x3+108x-144x2+324
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25 tháng 1 2023 lúc 16:17
Phân tích đa thức thành nhân tử A. 4x^2-12xy+9y^2-8x+12y B. 3x^2+20x-7 C. (3x-1)^4+2(9y^2-6x+1)+1 D. 2x^3-3x^2+2x-1
a: =(2x-3y)^2-4(2x-3y)
=(2x-3y)(2x-3y-4)
b: =3x^2+21x-x-7
=(x+7)(3x-1)
c: =(3x-1)^4+2(3x-1)^2+1
=[(3x-1)^2+1]^2
d: =2x^3-2x^2-x^2+x+x-1
=(x-1)(2x^2-x+1)
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Phân tích các đa thức sau thành nhân tử
a)x^2.(y-z)+y^2.(z-x)+z^2.(x-y)
b) (2x+5)^2-(x-9)^2
c)(2x+3)^2- 25.(x-1)^2
d)(4x^2-3x-18)^2-(4x^2+3x)^2
e)-4x^2+12xy-9y^2+25
f) 8x^2-2
g)8x^3-64
h)125x^3+1
Phân tích các đa thức sau thành nhân tửa) ^{ }3xy-6xy^2 b) ^{ }3x^3+6x^2+3xc) ^{ }x^3-x^2+2d) ^{ }x^2+4x+4-y^2e) ^{ }x^3+4x^2+4xf) ^{ }x^2+2x+1-9y^2g) ^{ }6x^2-12xh) ^{ }x^3+2x^2-xi) ^{ }x^2-2xy+y^2-9j) ^{ }x^2+x-6k) ^{ }2x^3+2x^2y-4xy^2l) ^{ }x^3-4x^2-12x+27
Đọc tiếp
Phân tích các đa thức sau thành nhân tử
a) \(^{ }3xy-6xy^2\)
b) \(^{ }3x^3+6x^2+3x\)
c) \(^{ }x^3-x^2+2\)
d) \(^{ }x^2+4x+4-y^2\)
e) \(^{ }x^3+4x^2+4x\)
f) \(^{ }x^2+2x+1-9y^2\)
g) \(^{ }6x^2-12x\)
h) \(^{ }x^3+2x^2-x\)
i) \(^{ }x^2-2xy+y^2-9\)
j) \(^{ }x^2+x-6\)
k) \(^{ }2x^3+2x^2y-4xy^2\)
l) \(^{ }x^3-4x^2-12x+27\)
a) \(3xy-6xy^2=3xy\left(1-2y\right)\)
b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)
c) \(x^3-x^2+2\)
d) \(x^2+4x+4-y^2=\left(x^2+4x+4\right)-y^2=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\)
e) \(x^3+4x^2+4x=x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)
f) \(x^2+2x+1-9y^2=\left(x+1\right)^2-\left(3y\right)^2=\left(x-3y+1\right)\left(x+3y+1\right)\)
g) \(6x^2-12x=6x\left(x-2\right)\)
h) \(x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\)
i) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)
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k) \(2x^3+2x^2y-4xy^2=2x\left(x^2+xy-2y^2\right)\)
l) \(x^3-7x^2+9x+3x^2-21x+27=x\left(x^2-7x+9\right)+3\left(x^2-7x+9\right)=\left(x+3\right)\left(x^2-7x+9\right)\)
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Câu 2: Phân tích các đa thức sau thành nhân tử :
a) (3x-1)^2-16
b) (5x-4)^2 -49x^2
c) (2x+5)^2 -(x-9)^2
d) (3x+1)^2 -4(x-2)^2
e) 9(2x+3)^2 -4(x+1)^2
f) 4b^2c^2-(b^2+c^2-a^2)^2
g) (ax+by)^2 - (ay+bx)^2
h) (a^2+b^2-5)^2 -4(ab+2)^2
i) (4x^2-3x-18)^2 -(4x^2+3x)^2
k) 9(x+y-1)^2 -4(2x+3y+1)^2
l) -4x^2 +12xy-9y^2+25
m) x^2-2xy+y^2-4m^2+4mn-n^2
\(a,\left(3x-1\right)^2-16=\left(3x-5\right)\left(3x+3\right)=3\left(x+1\right)\left(3x-5\right)\)
\(b,\left(5x-4\right)^2-49x^2=\left(12x-4\right)\left(-2x-4\right)=4\left(3x-1\right)\left(-2\right)\left(x+2\right)=-8\left(3x-1\right)\left(x+2\right)\)\(c,\left(2x+5\right)^2-\left(x-9\right)^2=\left(3x-4\right)\left(x+14\right)\)
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a,\(\left(3x+1\right)^2-16=\left(3x-1-16\right)\left(3x-1+16\right)\\ =\left(3x-17\right)\left(3x+15\right)\)
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Phân tích các đa thức sau thành nhân tử :
a, ( 3x -1 )^2 - 16
b, ( 5x-4 )^2 - 49x^2
c, ( 2x+5 )^2 - ( x-9 )^2
d, ( 3x + 1 )^2 - 4(x-2)^2
e, 9( 2x + 3 )^2 - 4( x + 1 )^2
f, 4b^2 c^2 - ( b^2 + c^2 - a^2 )^2
g, ( ax +by )^2 - ( ay + bx )^2
h, ( a^2 + b^2 - 5 )^2 - 4( ab + 2 )^2
i, ( 4x^2 - 3x - 18 )^2 - ( 4x^2 + 3x )^2
k, 9 ( x+y-1 )^2 - 4( 2x + 3y + 1)^2
l, -4x^2 + 12xy - 9y^2 + 25
m, x^2 - 2xy + y^2 - 4m^2 + 4mn - n^2
Giúp mình với ạ mình đang cần gấp
Đọc tiếp
Phân tích các đa thức sau thành nhân tử :
a, ( 3x -1 )^2 - 16
b, ( 5x-4 )^2 - 49x^2
c, ( 2x+5 )^2 - ( x-9 )^2
d, ( 3x + 1 )^2 - 4(x-2)^2
e, 9( 2x + 3 )^2 - 4( x + 1 )^2
f, 4b^2 c^2 - ( b^2 + c^2 - a^2 )^2
g, ( ax +by )^2 - ( ay + bx )^2
h, ( a^2 + b^2 - 5 )^2 - 4( ab + 2 )^2
i, ( 4x^2 - 3x - 18 )^2 - ( 4x^2 + 3x )^2
k, 9 ( x+y-1 )^2 - 4( 2x + 3y + 1)^2
l, -4x^2 + 12xy - 9y^2 + 25
m, x^2 - 2xy + y^2 - 4m^2 + 4mn - n^2
Giúp mình với ạ mình đang cần gấp
a) Ta có: \(\left(3x-1\right)^2-16\)
\(=\left(3x-1-4\right)\left(3x-1+4\right)\)
\(=\left(3x-5\right)\left(3x+3\right)\)
\(=3\left(x+1\right)\left(3x-5\right)\)
b) Ta có: \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)
\(=\left(-2x-4\right)\left(12x-4\right)\)
\(=-2\left(x+2\right)\cdot4\cdot\left(3x-1\right)\)
\(=-8\left(x+2\right)\left(3x-1\right)\)
c) Ta có: \(\left(2x+5\right)^2-\left(x-9\right)^2\)
\(=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\)
\(=\left(x+14\right)\left(3x-4\right)\)
d) Ta có: \(\left(3x+1\right)^2-4\left(x-2\right)^2\)
\(=\left(3x+1\right)^2-\left(2x-4\right)^2\)
\(=\left(3x+1-2x+4\right)\left(3x+1+2x-4\right)\)
\(=\left(x+5\right)\left(5x-3\right)\)
e) Ta có: \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)
\(=\left(6x+9\right)^2-\left(2x+2\right)^2\)
\(=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)\)
\(=\left(4x+7\right)\left(8x+11\right)\)
f) Ta có: \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\)
\(=-\left(b^2-2bc+c^2-a^2\right)\left[\left(b^2+2bc+c^2\right)-a^2\right]\)
\(=-\left[\left(b-c\right)^2-a^2\right]\cdot\left[\left(b+c\right)^2-a^2\right]\)
\(=-\left(b-c-a\right)\left(b-c+a\right)\left(b+c-a\right)\left(b+c+a\right)\)
g) Ta có: \(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(=\left(ax+by-ay-bx\right)\left(ax+by+ay+bx\right)\)
\(=\left[a\left(x-y\right)+b\left(y-x\right)\right]\left[a\left(x+y\right)+b\left(x+y\right)\right]\)
\(=\left[a\left(x-y\right)-b\left(x-y\right)\right]\left(x+y\right)\left(a+b\right)\)
\(=\left(x-y\right)\left(a-b\right)\left(x+y\right)\left(a+b\right)\)
h) Ta có: \(\left(a^2+b^2-5\right)^2-4\left(ab+2\right)^2\)
\(=\left(a^2+b^2-5\right)^2-\left(2ab+4\right)^2\)
\(=\left(a^2+b^2-5+2ab+4\right)\left(a^2+b^2-5-2ab-4\right)\)
\(=\left[\left(a^2+2ab+b^2\right)-1\right]\left[\left(a^2-2ab+b^2\right)-9\right]\)
\(=\left(a+b-1\right)\left(a+b+1\right)\left(a-b-3\right)\left(a-b+3\right)\)
i) Ta có: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)
\(=\left(-6x-18\right)\left(8x^2-18\right)\)
\(=-6\left(x+3\right)\cdot2\left(x^2-9\right)\)
\(=-12\left(x+3\right)^2\cdot\left(x-3\right)\)
k) Ta có: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)
\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)
\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)
\(=\left(-x-3y-5\right)\left(7x+9y-1\right)\)
l) Ta có: \(-4x^2+12xy-9y^2+25\)
\(=-\left(4x^2-12xy+9y^2-25\right)\)
\(=-\left[\left(2x-3y\right)^2-5^2\right]\)
\(=-\left(2x-3y-5\right)\left(2x-3y+5\right)\)
m) Ta có: \(x^2-2xy+y^2-4m^2+4mn-n^2\)
\(=\left(x-y\right)^2-\left(4m^2-4mn+n^2\right)\)
\(=\left(x-y\right)^2-\left(2m-n\right)^2\)
\(=\left(x-y-2m+n\right)\left(x-y+2m-n\right)\)
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Phân tích đa thức thành nhân tử:a) (3x - 1)2 - 16b) (5x - 4)2 - 49x2c) (2x + 5)2 - ( x - 9)2d) (3x + 1)2 - 4(x - 2)2 e) 9(2x + 3)2 - 4(x + 1)2f) 4b2c2 - (b2 + c2 - a2) 2g) (ax + by)2 - (ay + bx)2h) (a2 + b2 - 5)2 - 4(ab + 2)2i) (4x2 - 3x + 18)2 - (4x2 + 3x)2k) 9(x + y - 1)2 - 4(2x + 3y + 1)2e) -4x2 + 12xy - 9x2 + 25m) x2 - 2xy + y2 - 4m2 + 4mn - n2
Đọc tiếp
Phân tích đa thức thành nhân tử:
a) (3x - 1)2 - 16
b) (5x - 4)2 - 49x2
c) (2x + 5)2 - ( x - 9)2
d) (3x + 1)2 - 4(x - 2)2
e) 9(2x + 3)2 - 4(x + 1)2
f) 4b2c2 - (b2 + c2 - a2) 2
g) (ax + by)2 - (ay + bx)2
h) (a2 + b2 - 5)2 - 4(ab + 2)2
i) (4x2 - 3x + 18)2 - (4x2 + 3x)2
k) 9(x + y - 1)2 - 4(2x + 3y + 1)2
e) -4x2 + 12xy - 9x2 + 25
m) x2 - 2xy + y2 - 4m2 + 4mn - n2
\(a,=\left(3x-5\right)\left(3x+3\right)=3\left(x+1\right)\left(3x-5\right)\\ b,=\left(5x-4-7x\right)\left(5x-4+7x\right)=\left(-2x-4\right)\left(12x-4\right)\\ =-8\left(x+2\right)\left(x-3\right)\\ c,=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\\ =\left(x+14\right)\left(3x-4\right)\\ d,=\left(3x+1-2x+4\right)\left(3x+1+2x-4\right)\\ =\left(x+5\right)\left(5x-3\right)\\ e,=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)\\ =\left(4x+7\right)\left(8x+11\right)\\ f,=\left(2bc-b^2-c^2+a^2\right)\left(2bc+b^2+c^2-a^2\right)\\ =\left[a^2-\left(b-c\right)^2\right]\left[\left(b+c\right)^2-a^2\right]\\ =\left(a-b+c\right)\left(a+b-c\right)\left(b+c-a\right)\left(b+c+a\right)\\ g,=\left(ax+by-ay-bx\right)\left(ax+by+ay+bx\right)\\ =\left(a-b\right)\left(x-y\right)\left(a+b\right)\left(x+y\right)\)
\(h,=\left(a^2+b^2-5-2ab-4\right)\left(a^2+b^2-5+2ab+4\right)\\ =\left[\left(a-b\right)^2-9\right]\left[\left(a+b\right)^2-1\right]\\ =\left(a-b-3\right)\left(a-b+3\right)\left(a+b-1\right)\left(a+b+1\right)\)
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a: \(\left(3x-1\right)^2-16\)
\(=\left(3x-1-4\right)\left(3x-1+4\right)\)
\(=\left(3x+3\right)\left(3x-5\right)\)
\(=3\left(x+1\right)\left(3x-5\right)\)
b: \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)
\(=\left(-2x-4\right)\left(12x-4\right)\)
\(=-8\left(x+2\right)\left(3x-1\right)\)
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