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a) x4+2x2+1=(x2+1)2
b)=3x2(a+b)+x(a+b)+5(a+b)=(a+b)(3x2+x+5)
c)=x2(a-b)-2x(a-b)-3(a-b)=(a-b)(x2-2x-3)=(a-b)(x-3)(x+1)
d)=2x(y2-a2)-5by(y+a)=(y+a)(2xy-2xa-5by)
\(\text{a) x}^4+2x^2+1=\left(x^2+1\right)^2\)
\(\text{b) 3}ax^2+3bx^2+ãx+bx+5a+5b=\left(3ax^2+3bx^2\right) +\left(ax+bx\right)+\left(5a+5b\right)=3x^2+x\left(a+b\right)+5\left(a+b\right)=\left(a+b\right)\left(3x^2+x+5\right)\)
\(\text{c) a}x^2-bx^2-2ax+2bx-3a+3b=\left(\text{a}x^2-bx^2\right)-\left(2ax-2bx\right)-\left(3a-3b\right)=x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a-b\right)=\left(x^2-2x-3\right)\left(a-b\right)\)
A = 4acx + 4bcx + 4ax + 4bx ( đã sửa '-' )
= 4x( ac + bc + a + b )
= 4x[ c( a + b ) + ( a + b ) ]
= 4x( a + b )( c + 1 )
B = ax - bx + cx - 3a + 3b - 3c
= x( a - b + c ) - 3( a - b + c )
= ( a - b + c )( x - 3 )
C = 2ax - bx + 3cx - 2a + b - 3c
= x( 2a - b + 3c ) - ( 2a - b + 3c )
= ( 2a - b + 3c )( x - 1 )
D = ax - bx - 2cx - 2a + 2b + 4c
= x( a - b - 2c ) - 2( a - b - 2c )
= ( a - b - 2c )( x - 2 )
E = 3ax2 + 3bx2 + ax + bx + 5a + 5b
= 3x2( a + b ) + x( a + b ) + 5( a + b )
= ( a + b )( 3x2 + x + 5 )
F = ax2 - bx2 - 2ax + 2bx - 3a + 3b
= x2( a - b ) - 2x( a - b ) - 3( a - b )
= ( a - b )( x2 - 2x - 3 )
= ( a - b )( x2 + x - 3x - 3 )
= ( a - b )[ x( x + 1 ) - 3( x + 1 ) ]
= ( a - b )( x + 1 )( x - 3 )
Ta có
2 a 2 x – 5 b y – 5 a 2 y + 2 b x = 2 a 2 x – 5 a 2 y + 2 b x – 5 b y = a 2 2 x – 5 y + b 2 x – 5 y = a 2 + b 2 x – 5 y
Đáp án cần chọn là: D
\(1,2x^2-6xy+5x-15y\)
\(=2x\left(x-3y\right)+5\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x+5\right)\)
\(2,ax^{2\:}-3axy+bx-3by\)
\(=ax\left(x-3y\right)+b\left(x-3y\right)\)
\(=\left(x-3y\right)\left(ax+b\right)\)
\(3,5ax^2-3axy+3ay^2-3axy\) ( Đề sai )
Sửa : \(3ax^2-3axy+3ay^2-3axy\)
\(=3ax\left(x-y\right)+3ay\left(y-x\right)\)
\(=3ax\left(x-y\right)-3ay\left(x-y\right)\)
\(=3a\left(x-y\right)^2\)
\(4,4acx+4bcx+4ax+4bx\)
\(=4cx\left(a+b\right)+4x\left(a+b\right)\)
\(=4x\left(a+b\right)\left(c+1\right)\)
\(6,ax^{2\:}y-bx^2y-ax+bx+2a-2b\)
\(=x^2y\left(a-b\right)-x\left(a-b\right)+2\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2y-x+2\right)\)
\(7,ax^{2\:}-bx^2-2ax+2bx-3a+3b\)
\(=x^2\left(a-b\right)-2x\left(a-b\right)-3\left(a-b\right)\)
\(=\left(a-b\right)\left(x^2-2x-3\right)\)
\(8,ax^{2\:}-5x^2-ax+5x+a-5\)
\(=x^2\left(a-5\right)-x\left(a-5\right)+\left(a-5\right)\)
\(=\left(a-5\right)\left(x^2-x+1\right)\)
\(9,ax+bx+cx-2a-2b+2c\) Đề sai
Sửa :\(ax+bx+cx-2a-2b-2c\)
\(=x\left(a+b+c\right)-2\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(x-2\right)\)
\(10,2ax-bx+3cx-2a+b-3c\)
\(=\left(2ax-2a\right)-\left(bx-b\right)+\left(3cx-3c\right)\)
\(=2a\left(x-1\right)-b\left(x-1\right)+3c\left(x-1\right)\)
\(=\left(x-1\right)\left(2a-b+3c\right)\)
Mấy câu đề sai mk sửa chỗ nào ko đúng thì nói mk nha !
a, x(a - b) + (a - b)
= (x + 1)(a - b)
b, x(a + b) - a - b
= x(a + b) - (a + b)
= (x - 1)(a + b)
c, 10ax - 5ay - 2x + y
= 5a(2x - y) - (2x - y)
= (5a - 1)(2x - y)
d, 2a^2x - 5by - 5a^2y + 2bx
= 2x(a^2 + b) - 5y(b + a^2)
= (2a - 5y)(a^2 + b)
làm tiếp:
2ax2 - bx2 - 2ax +bx +4a-2b
= x2(2a-b) - x(2a-b) +2(2a-b)
=(2a-b)(x2-x+2)
4acx + 4bcx + 4ax + 4bx
= 4cx ( a+ b) + 4x ( a+b)
= 4x ( c +1 )(a +b)
Phân tích đa thức thành nhân tử:
\(4acx+4bcx+4ax+4bx\)
\(=\left(4acx+4ax\right)+\left(4bcx+4bx\right)\)
\(=4ax\left(c+1\right)+4bx\left(c+1\right)\)
\(=\left(4ax+4bx\right)\left(c+1\right)\)
\(=4x\left(a+b\right)\left(c+1\right)\)
Lời giải:
31.
\(2a^2x-5by-6a^2y+2bx=(2a^2x+2bx)-(5by+5a^2y)\)
\(=2x(a^2+b)-5y(b+a^2)=(a^2+b)(2x-5y)\)
34.
\(4acx+4bcx+4ax+4bx=4x(ac+bc+a+b)\)
\(=4x[(ac+bc)+(a+b)]=4x[c(a+b)+(a+b)]=4x(c+1)(a+b)\)
37. Sửa đề:
\(2ax^2-bx^2-2ax+bx+4a-2b\)
\(=(2ax^2-bx^2)-(2ax-bx)+(4a-2b)\)
\(=x^2(2a-b)-x(2a-b)+2(2a-b)=(2a-b)(x^2-x+2)\)
Câu 31:
\(2a^2x-5by-5a^2y+2bx\)
\(=2x\left(a^2+b\right)-5y\left(a^2+b\right)\)
\(=\left(a^2+b\right)\left(2x-5y\right)\)
Câu 34:
\(4acx+4bcx+4ax+4bx\)
\(=4cx\left(a+b\right)+4x\left(a+b\right)\)
\(=\left(a+b\right)\left(4cx+4x\right)\)
\(=4x\left(a+b\right)\left(c+1\right)\)
Câu 37:
\(2ax^2-bx^2-2ax+bx+4a-2b\)
\(=x^2\left(2a-b\right)-x\left(2a-b\right)+2\left(2x-b\right)\)
\(=\left(2a-b\right)\left(x^2-x+2\right)\)
\(=\left(2a-b\right)\left(x^2-x+2\right)\)