Toán Lớp 8: Phân tích thành nhân tử
a) x^3 – 2x^2 + x.
b) 2x^2 + 4x + 2 – 2y^2
c) 2xy – x^2 – y^2 + 16
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Toán Lớp 8: Phân tích thành nhân tử
a) x^3 – 2x^2 + x.
b) 2x^2 + 4x + 2 – 2y^2
c) 2xy – x^2 – y^2 + 16
Comments ( 2 )
Giải đáp + giải thích các bước giải:
a) x^3 – 2x^2 + x
= x(x^2 – 2x + 1)
= x(x – 1)^2
b) 2x^2 + 4x + 2 – 2y^2
= 2(x^2 + 2x + 1 – y^2)
= 2[(x + 1) – y^2]
= 2(x + 1 – y)(x + 1 + y)
c) 2xy – x^2 – y^2 + 16
= -(x^2 – 2xy + y^2 – 16)
= -[(x – y)^2 – 4^2)
= -(x – y – 4)(x – y + 4)
$ a) x^3 – 2x^2 + x = x(x^2-2x+1) = x(x-1)^2 $
$ b) 2x^2 + 4x + 2 – 2y^2 = 2(x^2+2x+1-y^2)=2[(x^2+2x+1)-y^2]=2[(x+1)^2-y^2]=2(x + 1 – y)(x + 1 + y) $
$ c) 2xy – x^2 – y^2 + 16 = 16 – (x^2-2xy+y^2)=4^2-(x-y)^2=[4-(x-y)][4+(x-y)]=(4-x+y)(4+x-y) $