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\(10x^2-1=\left(\sqrt{10}x-1\right)\left(\sqrt{10}x+1\right)\)
\(9a^2-6ab+b^2-1=\left(3a-b\right)^2-1^2=\left(3a-b-1\right)\left(3a-b+1\right)\)
9a^2 - 6ab + b^2 - 1= (3a)^2 - 2.3a.b + b^2 -1
= (3a - b)^2 - 1^2
= (3a - b - 1).(3a - b + 1)
Ta có
a, x2-x-y2-y
=x2-y2-(x+y)
=(x-y)(x+y) - (x+y)
=(x+y)(x-y-1)
b, x2-2xy+y2-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
4x^4 - 32x^2 +1 = 4x^4 + 4x^2 +1 - 36x^2 = (2x^2 + 1)^2 - 36x^2 = (2x^2 - 6x + 1)(2x^2 + 6x + 1)
4 x4 - 32 x2 + 1
= ( 2 x2 )2 - 2 . 2x2. 8 + 64 - 63
= ( 2 x2 - 8 )2 - 63
= ( 2x2 - 8 + √63 ) ( 2x2 - 8 - √63 )
Xong
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)
\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)
\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)
\(=\left(x^2+x+5\right)\left(x+2\right)\left(x-1\right)\)
\(\left(3x+1\right)^2-\left(x+1\right)^2\)
\(=\left(3x+1+x+1\right)\left(3x+1-x-1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)
(3x+1)2-(x+1)2
=[(3x+1)-(x+1)][(3x+1)+(x+1)]
=[3x+1-x-1][3x+1+x+1]
=[2x][4x+2]
=2x*[2(2x+1)]
=4x(2x+1)
\(4x^2-4x+1\)\(=\) \((2x^2)-2.2x.1+1^2\)
\(=\left(2x-1\right)^2\)
Học tốt!
\(1-3x-x^3+3x^2\)\(=\left(1-x^3\right)+\left(3x^2-3x\right)\)
\(=\left(1-x\right)\left(x^2+x+1\right)+3x\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-x^2-x-1\right)=\left(x-1\right)\left(2x-x^2-1\right)\)