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a/x2(x+1)-2x(x+1)+(x+1)=(x+1)(x^2-2x+1)=(x+1)(x-1)^2
b/a2+b2+2a-2b-2ab=(a^2-ab)+(b^2-ab)+2(a-b)=a(a-b)-b(a-b)+2(a-b)=(a-b)(a-b+2)
c/ 4x2-8x+3=(2x-2)^2-1=(2x-2-1)(2x-2+1)=(2x-3)(2x-1)
d/25-16x2=5^2-(4x)^2=(5-4x)(5+4x)
Lời giải:
a)
$70a-84b-20ab-24b^2=2(35a-42b-10ab-12b^2)$
b)
$12y-9x^2+36-3x^2y$
$=(12y-3x^2y)+(36-9x^2)$
$=3y(4-x^2)+9(4-x^2)$
$=(3y+9)(4-x^2)=3(y+3)(2-x)(2+x)$
c)
$21bc^2-6c-3c^2+42b=3(7bc^2-2c-c^2+14b)$
d)
$30a^3-18a^2b-72b+120a$
$=(30a^3+120a)-(18a^2b+72b)$
$=30a(a^2+4)-18b(a^2+4)$
$=(a^2+4)(30a-18b)=6(a^2+4)(5a-3b)$
P/s: Cảm giác câu a,c bạn viết sai đề.
a^2 + b^2 - 2a + 2b - 2ab
= (a^2 - 2ab + b^2) - 2(a - b)
= (a - b)^2 - 2(a - b)
= (a - b)(a - b - 2)
a^2+b^2-2a+2b-2ab
=(a^2+b^2-2ab)-(2a-2b)
=(a-b)^2-2(a-b)
=(a-b)(a-b-2)
a) a2 + b2 + 2ab + 2a + 2b + 1
= (a2 + b2 + 2ab) + (2a + 2b) + 1
= (a + b)2 + 2(a + b) + 1
= (a + b + 1)2
b) a3 - 3a + 3b - b3
= (a3 - b3) - (3a - 3b)
= (a - b)(a2 - ab + b2) - 3(a - b)
= (a - b)(a2 - ab + b2 - 3)
c) x2 + 2x - 15
= (x2 + 2x + 1) - 16
= (x + 1)2 - 16
= (x + 1 - 5)(x + 1 + 5)
= (x - 4)(x + 6)
d) a4 + 6a2b + 9b2 - 1
= (a2 + 3b)2 - 1
= (a2 + 3b - 1)(a2 + 3b + 1)
2a2b2+2a2c2+2b2c2-a4-b4-c4
=4a2b2-(a4+2a2b2+b4)+(2b2c2+2a2c2)-c4
=2(ab)2-(a+b)2+2c2(a2+b2)+c4
=2(ab)2-[(a+b)2-2c2(a2+b2)+c4]
=2(ab)2-(b2+a2-c2)2
=[(a+b)2-c2][-(a-b)2+c2]
=(a+b-c)(a+b+c)(c-a+b)(a+c-b)
\(2a^2b^2+2a^2c^2+2b^2c^2-a^4-b^4-c^4\)
\(=4a^2b^2-\left(a^4+2a^2b^2+b^4\right)+\left(2b^2c^2+2a^2c^2\right)-c^4\)
\(=2\left(ab\right)^2-\left(a+b\right)^2+2c^2\left(a^2+b^2\right)+c^4\)
\(=2\left(ab\right)^2-\left[\left(a+b\right)^2-2c^2\left(a^2+b^2\right)+c^4\right]\\ =2\left(ab\right)^2-\left(b^2+a^2-c^2\right)^2\)
=\(\left[\left(a+b\right)^2-c^2\right]\left[-\left(a-b\right)^2+c^2\right]\\ =\left(a+b+c\right)\left(a+b+c\right)\left(c-a+b\right)\left(a+c-b\right)\)
a ) 2a2b2 + 2b2c2 + 2a2c2 - a4 - b4 - c4
= 4a2b2 - 2a2b2 + 2b2c2 + 2a2c2 - a4 - b4 - c4
= 4a2b2 - ( a4 + 2a2b2 + b4 ) + ( 2b2c + 2a2c2 ) - c4
= 4a2b2 - [ ( a2 + b2 ) - 2.c2. ( b2 + a2 ) + c4 ]
= ( 2ab )2 - ( a2 + b2 - c2 )
= ( 2ab - a2 - b2 + c2 )( 2ab + a2 + b2 - c2 )
= [ c2 - ( a2 - 2ab + b2 ) ] . [ (a2 + 2ab + b2 ) - c2 ]
= [ c2 - ( a - b )2 ] . [ ( a + b )2 - c2 ]
= ( c - a + b )( c + a - b )( a + b - c )( a + b + c )
b ) x2 - 10x + 24
= ( x2 - 10x + 25 ) - 1
= ( x - 5 )2 - 12
= ( x - 5 - 1 )( x - 5 + 1 )
= ( x - 6 )( x - 4 )
a2 + b2 + 2ab + 2a + 2b + 1
= ( a2 + 2ab + b2 ) + ( 2a + 2b ) + 1
= ( a + b )2 + 2( a + b ) + 12
= ( a + b + 1 )2
3x( x - 2y ) - 6y( 2y - x )
= 3x( x - 2y ) + 6y( x - 2y )
= 3( x - 2y )( x + 2y )
x2 + 2x - 3
= x2 - x + 3x - 3
= x( x - 1 ) + 3( x - 1 )
= ( x - 1 )( x + 3 )
a) \(a^2+b^2+2ab+2a+2b+1\)
\(=\left(a^2+2ab+b^2\right)+\left(2a+2b\right)+1\)
\(=\left(a+b\right)^2+2\left(a+b\right)+1\)
\(=\left(a+b+1\right)^2\)
b) \(3x\left(x-2y\right)-6y\left(2y-x\right)\)
\(=3x\left(x-2y\right)+6y\left(x-2y\right)\)
\(=3\left(x-2y\right)\left(x+2y\right)\)
c) \(x^2+2x-3=x^2-x+3x-3\)
\(=\left(x^2-x\right)+\left(3x-3\right)\)
\(=x\left(x-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x+3\right)\)
a ) Sai đề : \(21bc^2+6c+3c^3+42b\)
\(=3c^2\left(7b+c\right)+6\left(7b+c\right)\)
\(=\left(3c^2+6\right)\left(7b+c\right)\)
\(=3\left(c^2+2\right)\left(7b+c\right)\)
b ) \(a^2+b^2+2a-2b-2ab\)
\(=\left(a^2-2ab+b^2\right)+2\left(a-b\right)\)
\(=\left(a-b\right)\left(a-b+2\right)\)
c ) \(x^2-5x+4\)
\(=x^2-4x-x+4\)
\(=x\left(x-4\right)-\left(x-4\right)\)
\(=\left(x-1\right)\left(x-4\right)\)
a)Sai đề nha bạn
\(21bc^2+6c+3c^3+42b=3c^2\left(7b+3c\right)+6\left(7b+c\right)=\left(3c^2+6\right)\left(7b+c\right)\)
b)\(a^2+b^2+2a-2b-2ab=a^2-2ab+b^2+2a-2b=\left(a-b\right)^2+2\left(a-b\right)=\left(a-b\right)\left(a-b+2\right)\)
c)\(x^2-5x+4=x^2-x-4x+4=x\left(x-1\right)-4\left(x-1\right)=\left(x-4\right)\left(x-1\right)\)