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a) (x-1)(2x+5)
b) (x+1)(x-5)
c) [(x+1)^2](x^2+x+1)
d) (x-1)(x^3-x-1)
e) (x+y)(x-y-1)
a) 2x2 + 3x - 5 = 2x2 + 5x - 2x - 5 = x(2x + 5) - (2x + 5) = (x - 1)(2x + 5)
b) x2 - 4x - 5 = x2 - 5x + x - 5 = x(x - 5) + (x - 5) = (x + 1)(x - 5)
c) x4 + x3 + x + 1 = x3(x + 1) + (x + 1) = (x + 1)(x3 + 1) = (x + 1)2(x2 - x + 1)
d) x4 - x3 - x2 + 1 = x3(x - 1) - (x - 1)(x + 1) = (x - 1)(x3 - x - 1)
e) -x - y2 + x2 - y = -(x + y) + (x - y)(x + y) = (-1 + x - y)(x + y)
Bài làm:
a) \(2x^2+7x+5=\left(2x^2+2x\right)+\left(5x+5\right)=2x\left(x+1\right)+5\left(x+1\right)\)
\(=\left(2x+5\right)\left(x+1\right)\)
b) \(x^3-2x-4=\left(x^3-2x^2\right)+\left(2x^2-4x\right)+\left(2x-4\right)\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)=\left(x-2\right)\left(x^2+2x+2\right)\)
c) \(x^2+4x+3=\left(x^2+x\right)+\left(3x+3\right)=x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(x+3\right)\)
2x2 + 7x + 5 = 2x2 + 2x + 5x + 5 = ( 2x2 + 2x ) + ( 5x + 5 ) = 2x( x + 1 ) + 5( x + 1 ) = ( 2x + 5 )( x + 1 )
x2 + 4x + 3 = x2 + x + 3x + 3 = ( x2 + x ) + ( 3x + 3 ) = x( x + 1 ) + 3( x + 1 ) = ( x + 3 )( x + 1 )
\(giải:\)
\(16x^2y-4xy^2-4x^3+x^2y\)
\(=\left(16x^2y-4xy^2\right)-\left(4x^3-x^2y\right)\)
\(=4xy\left(4x-y\right)-x^2\left(4x-y\right)\)
\(=\left(4x-y\right)\left(4xy-x^2\right)\)
\(=\left(4x-y\right)\left(\sqrt{4xy}-x\right)\left(\sqrt{4xy}+x\right)\)
\(=\left(4x-y\right)\left(2\sqrt{xy}-x\right)\left(2\sqrt{xy}+x\right)\)
a. \(x^5+x+1\)
\(=\left(x^5-x^2\right)+x^2+x+1\)
\(=x^2\left(x^3-1\right)+x^2+x+1\)
\(=x^2\left(x-1\right)\left(x^2+x+1\right)\)\(+x^2+x+1\)
\(=\left[x^2\left(x-1\right)+1\right]\left(x^2+x+1\right)\)
\(=\left(x^3-x^2+1\right)\left(x^2+x+1\right)\)
b.\(x^3+x^2+4\)
=\(x^3+2x^2-x^2-2x+2x+4\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+2\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-x+2\right)\)
c.\(x^4+2x^2-24\)
\(=x^4+2x^3-2x^3-4x^2+6x^2+12x-12x-24\)
\(=x^3\left(x+2\right)-2x^2\left(x+2\right)+6x\left(x+2\right)-12\left(x+2\right)\)
\(=\left(x^3-2x^2+6x-12\right)\left(x+2\right)\)
\(=\left[x^2\left(x-2\right)+6\left(x-2\right)\right]\left(x+2\right)\)
\(=\left(x^2+6\right)\left(x-2\right)\left(x+2\right)\)
a, x^5 + x + 1 = x ^ 5 - x^2 + (x ^2 + x + 1) = x^2 ( x-1) ( x^2+x+1) + ( x^2+x+1) = ( x^2+x+1 ) ( x^3-x^2+1)
c, x^4 + 2x^2 -24 = (x^4 +6x^2) - ( 4x^2+24) = x^2( x^2+6) - 4(x^2+6) = (x^2-4)(x^2 +6 ) = (x-2)(x+2)(x^2+6)
\(x^4-y^4=\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)
\(1^2-2^2+3^2-....-100^2=\left(1^2-2^2\right)+...+\left(99^2-100^2\right)=\)
\(-1\left(1+2\right)+\left(-1\right)\left(3+4\right)+...+\left(-1\right)\left(99+100\right)=\frac{-100.101}{2}=-5050\)
A = x^2 + 2. (x+y)^2 = 4y^2 + 2. ( 3y)^2 = 22y^2 = 22. ( 2 căn 2 ) ^2 = 176
B = - ( x+ 2y ) ^2 +7y^2 = - ( 4y)^2 + 7y^2 = -9 y^2 = -72
Bài 1 :
a)3x+6y
=3(x+y)
b)\(x^2-y^2-7x+7y\)
\(=\left(x-y\right)\left(x+y\right)-7\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-7\right)\)
câu c sai đề à
d)\(4x^2-4x-15\)
\(=\left(4x^2-4x+1\right)-16\)
\(=\left(2x-1\right)^2-16\)
\(=\left(2x-1-4\right)\left(2x-1+4\right)\)
\(=\left(2x-5\right)\left(2x+3\right)\)
a)3x+6y = 3( x + 2y )
b)x2−y2−7x+7y = x( x - 7 ) - y ( y - 7 )
= ( x - y ) ( x - 7 )
c) 3b−x2+4xy−4y2
= 3b - ( x\(^2\) - 4xy + 4y\(^2\)) = 3b - ( x - 2y )\(^2\) câu này hình như sai chỗ 3b phải ko
d)4x2−4x−15 = 4x\(^2\) - 10x + 6x -15 =0
= 2x ( 2x +3 ) - 5 ( 2x + 3 ) = 0
= ( 2x - 5 )( 2x + 3)
4x2−4x−15
a,x^2+4-16x^2
-15x^2+4
-(15x^2-4)
b,(1-2y+y^2)-(x^2-4xz+4z^2)
(1-y)^2-(x-z)^2
(1-y+x-z)(1-y-x+z)
c,(4x^2-4xy+y^2)-(25z^2-10z+1)
(2x+y)^2-(5z-1)^2
(2x+y+5z-1)(2x+y-5z+1)