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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)
\(x^2-3x+xy-3y\)
\(=\left(x^2+xy\right)-\left(3x+3y\right)\)
\(=x.\left(x+y\right)-3.\left(x+y\right)\)
\(=\left(x-3\right).\left(x+y\right)\)
\(2x^2-x+2xy-y\)
\(=2x^2-\left(x-2xy+y\right)\)
\(=2x^2-\left(x-y\right)^2\)
\(=\left(\sqrt{2}x\right)^2-\left(x-y\right)^2\)
\(=\left(\sqrt{2}x-x+y\right).\left(\sqrt{2}x+x-y\right)\)
\(x^4+x^3+2x^2+x+1\)
\(=\left(x^4+2x^2+1\right)+\left(x^3+x\right)\)
\(=\left(x^2+1\right)^2+x.\left(x^2+1\right)\)
\(=\left(x^2+1\right).\left(x^2+1+x\right)\)
\(16+2xy-x^2-y^2\)
\(=16-x^2+2xy-y^2\)
\(=16-\left(x^2-2xy+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=[4-\left(x-y\right)].[4+\left(x-y\right)]\)
\(=\left(4-x+y\right).\left(4+x-y\right)\)
\(a,xy+1-x-y\)
\(=\left(xy-y\right)+\left(1-x\right)\)
\(=y\left(x-1\right)- \left(x-1\right)\)
\(=\left(x-1\right)\left(y-1\right)\)
\(b,ax+ay-3x-3y\)
\(=a\left(x+y\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(a-3\right)\)
\(c,x^3-2x^2+2x-4\)
\(=x^2\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x^2+2\right)\left(x-2\right)\)
\(d,x^2+ab+ax+bx\)
\(=\left(x^2+ax\right)+\left(ab+bx\right)\)
\(=x\left(a+x\right)+b\left(a+x\right)\)
\(=\left(a+x\right)\left(b+x\right)\)
\(e,16-x^2+2xy-y^2\)
\(=4^2-\left(x^2-2xy+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)
1,a4 + a3b + a + b
=a3(a+b)+(a+b)
=(a+b)(a3+1)
=(a+b)(a+1)(a2-a+1)
2,x3 + 2x2 - 2x - 1
=(x3-1)+(2x2-2x)
=(x-1)(x2+x+1)+2x(x-1)
=(x-1)(x2+x+1+2x)
=(x-1)(x2+3x+1)
3,4x(x-3y) + 12y(3y-x)
=-4x(3y-x)+12y(3y-x)
=(3y-x)(-4x+12y)
4,(x2-8) + 36
=x2-8-36+72
=(x2-62)+64
=(x-6)(x+6)+64
5,(x + 2) + (x + 3) + (x + 4) + (x + 5) - 24
=x + 2 + x + 3 + x + 4 + x + 5 -24
=4x-10
6,x2 - 2xy + y2 + 3x - 3y -10
=(x-y)2+3(x-y)-10
=(x-y)(x-y+3)-10
câu 4,5,6 bạn làm sai rồi!