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a. \(2a^2+5ab-3b^2-7b-2\)
\(=\left(2a^2+6ab+2a\right)-\left(ab+3b^2+b\right)-\left(2a+6b+2\right)\)
\(=2a\left(a+3b+1\right)-b\left(a+3b+1\right)-2\left(a+3b+1\right)\)
\(=\left(2a-b-2\right)\left(a+3b+1\right)\)
b. \(2x^2-7xy+x+3y^2-3y\)
\(=\left(2x^2-xy\right)-\left(6xy-3y^2\right)+\left(x-3y\right)\)
\(=x\left(2x-y\right)-3y\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y+1\right)\)
c. \(6x^2-xy-2y^2+3x-2y\)
\(=\left(6x^2+3xy\right)-\left(4xy-2y^2\right)+\left(3x-2y\right)\)
\(=3x\left(2x+y\right)-2y\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y\right)+\left(3x-2y\right)\)
\(=\left(3x-2y\right)\left(2x+y+1\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a) ax - 2x - a2 + 2a
= ( ax - 2x ) - ( a2 - 2a )
= x ( a - 2 ) - a ( a - 2 )
= ( a - 2 ) ( x - a )
b) x2 + x - ax - a
= ( x2 + x ) - ( ax + a )
= x ( x + 1 ) - a ( x + 1 )
= ( x + 1 ) ( x - a )
Hok Tốt!!!
a) ax -2x- a2+ 2a
= (ax -2x ) -(a2 -2a )
= x(a-2) -a ( a-2 )
= (x-a) (a-2)
b) x2 +x -ax -a
=( x2 +x ) - ( ax +a )
= x( x+1 ) -a ( x+1 )
= ( x-a ) (x+ 1)
c) 2x2 +4ax +x +2a
=( 2x2 + 4ax ) + ( x+ 2a )
= 2x ( x+ 2a ) + ( x+2a )
= ( 2x +1 ) (x+2a )
d) 2xy -ax +x2 - 2ay
= (2xy -2ay ) + ( -ax + x2 )
= 2y( x-a ) + x ( x-a)
= ( 2y +x ) ( x -a )
Phân tích đa thức thành nhân tử
a) (1-2x)(1+2x)-x(x+2)(x-2)
\(=1-4x^2-x\left(x^2-4\right)\)
\(=1-4x^2-x^3+4x\)
\(=\left(1-x^3\right)+\left(4x-4x^2\right)\)
\(=\left(1-x\right)\left(1+x+x^2\right)+4x\left(1-x\right)\)
\(=\left(1-x\right)\left(1+x+x^2+4x\right)\)
\(=\left(1-x\right)\left(x^2+5x+1\right)\)
\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+12a^2b^2+8b^3a-8a^3b-12a^2b^2+6ab^3-b^4\)
\(=a^4+6a^3b+8b^3a-8a^3b-6ab^3-b^4\)
\(=\left(a^4-b^4\right)+\left(6a^3b-6ab^3\right)+\left(8b^3a-8a^3b\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3\right)+6ab\left(a^2-b^2\right)+8ab\left(b^2-a^2\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3\right)+6ab\left(a-b\right)\left(a+b\right)-8ab\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(a^3+a^2b+ab^2+b^3+6a^2b+6ab^2-8a^2b-8ab^2\right)\)
\(=\left(a-b\right)\left(a^3-a^2b-ab^2+b^3\right)\)
\(=\left(a-b\right)\left[a^2\left(a-b\right)-b^2\left(a-b\right)\right]\)
\(=\left(a-b\right)^3\left(a+b\right)\)
\(x^2-3x+xy-3y\)
\(=\left(x^2+xy\right)-\left(3x+3y\right)\)
\(=x.\left(x+y\right)-3.\left(x+y\right)\)
\(=\left(x-3\right).\left(x+y\right)\)
\(2x^2-x+2xy-y\)
\(=2x^2-\left(x-2xy+y\right)\)
\(=2x^2-\left(x-y\right)^2\)
\(=\left(\sqrt{2}x\right)^2-\left(x-y\right)^2\)
\(=\left(\sqrt{2}x-x+y\right).\left(\sqrt{2}x+x-y\right)\)
\(x^4+x^3+2x^2+x+1\)
\(=\left(x^4+2x^2+1\right)+\left(x^3+x\right)\)
\(=\left(x^2+1\right)^2+x.\left(x^2+1\right)\)
\(=\left(x^2+1\right).\left(x^2+1+x\right)\)
\(16+2xy-x^2-y^2\)
\(=16-x^2+2xy-y^2\)
\(=16-\left(x^2-2xy+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=[4-\left(x-y\right)].[4+\left(x-y\right)]\)
\(=\left(4-x+y\right).\left(4+x-y\right)\)
\(\left(2x^2+4xz-6xy\right)-\left(xy+2yz-3y^2\right)+\left(2z^2+xz-3yz\right)\)
\(2x\left(x+2z-3y\right)-y\left(x+2z-3y\right)+z\left(2z+x-3y\right)\)
\(\left(x+2z-3y\right)\left(2x-y+z\right)\)
1/Tự chép lại đb nha :v
=a2 - 9b2+2ab+3a2-8b2-12ab+6ab-3b2-2a2+ab
= 2a2-3ab-20b2
= (2a2+5ab) - (8ab+20b2)
= a(2a+5b) - 4b(2a+5b)
=(2a+5b)(a-4b)
câu 2 tương tự nhé :)
b: \(2x^2-7xy+3y^2+x-3y\)
\(=2x^2-6xy-xy+3y^2+x-3y\)
\(=2x\left(x-3y\right)-y\left(x-3y\right)+\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x-y+1\right)\)
Lời giải:
a.
Đặt $2a^2+5ab-3b^2-7b-2=(a+mb+n)(2a+pb+k)$ với $m,n,p,k$ nguyên
$\Leftrightarrow 2a^2+5ab-3b^2-7b-2=2a^2+ab(2m+p)+mpb^2+a(k+2n)+b(km+np)+kn$
Đồng nhất hệ số:
\(\left\{\begin{matrix} 2m+p=5\\ mp=-3\\ k+2n=0\\ km+np=-7\\ kn=-2\end{matrix}\right.\)
Giải hpt này ta thu được $m=3; n=1; p=-1; k=-2$
Vậy $2a^2+5ab-3b^2-7b-2=(a+3b+1)(2a-b-2)$
b. Đa thức không phân tích được thành nhân tử