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\(x^2y^2-x^2+8x-16.\)
\(=x^2y^2-x^2+4x+4x-16+x^2y-x^2y+4xy-4xy\)
\(=x^2y^2+x^2y-4xy-x^2y-x^2+4x+4xy+4x-16\)
\(=\left(x^2y^2+x^2y-4xy\right)-\left(x^2y+x^2-4x\right)+\left(4xy+4x-16\right)\)
\(=xy\left(xy+x-4\right)-x\left(xy+x-4\right)+4\left(xy+x-4\right)\)
\(=\left(xy+x-4\right)\left(xy-x+4\right)\)
a. 2x-1-x2= -(x2-2x+1)=-(x-1)2
b. 8x3+y6=(2x)3+(y2)3
=(2x+y2)(4x2-2xy2+y4)
c. x2-16+4xy+4y2=(x2+4xy+4y2)-16
=(x+2y)2-16=(x+2y+4)(x+2y-4)
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)
x2 - 2x + 2y - xy = (x2 - 2x) - (xy - 2y) = x(x - 2) - y(x - 2) = (x - 2)(x - y)
x2 + 4xy - 16 + 4y2 = (x2 + 4xy + 4y2) - 16 = (x + 2y)2 - 16 = (x + 2y + 4)(x + 2y - 4)
a)x^2-4xy+4y^2-4
=(x2-4xy+4y2)-4
=(x-2y)2-4
=(x-2y+2)(x-2y-2)
b)16-x^2+2xy-y^2
=16-(x2-2xy+y2)
=16-(x-y)2
=[4-(x-y)][4+(x-y)]
=(4-x+y)(4+x-y)
a, = (x^3-x^2)-(4x^2-4x)+(4x-4)
= (x-1).(x^2-4x+4) = (x-1).(x-2)^2
b, = (x^3+x^2)-(10x^2+10x)+(16x+16)
= (x+1).(x^2-10x+16)
= (x+1).[ (x^2-2x)-(8x-16) ] = (x+1).(x-2).(x-8)
k mk nha
a)= (x^3-x^2)-(4x^2-4x)+(4x-4)
= (x-1).(x^2-4x+4)
= (x-1).(x-2)^2
b)= (x^3+x^2)-(10x^2+10x)+(16x+16)
= (x+1).(x^2-10x+16)
= (x+1).[ (x^2-2x)-(8x-16) ]
= (x+1).(x-2).(x-8)
P/s tham khảo nha
\(x^4-4x^3+8x^2-16x+16 \)
\(=x^3\left(x-2\right)-2x^2\left(x-2\right)+4x\left(x-2\right)-8\left(x-2\right)\)
\(=\left(x-2\right)\left(x^3-2x^2+4x-8\right)\)
\(=\left(x-2\right)\left[x^2\left(x-2\right)+4\left(x-2\right)\right]\)
\(=\left(x-2\right)^2\left(x^2+4\right)\)