Toán Lớp 8: bài 1 phân tích đa thức thành nhân tử a)x^2+xy+4x+4y b)3xy+3x^2+7y+7x c)x^2-4x+4-y^2 d)xy-8y+x^2-8x e)4x^3-4x+x+1 g)2xy+4z+8y+xz h)y^2+

Question

Toán Lớp 8:  bài 1 phân tích đa thức thành nhân tử a)x^2+xy+4x+4y b)3xy+3x^2+7y+7x c)x^2-4x+4-y^2 d)xy-8y+x^2-8x e)4x^3-4x+x+1 g)2xy+4z+8y+xz h)y^2+10y+25-x^2 i)x^2-2^2-8x+16

phuongthuydung · Answer

Giải đáp:       Lời giải và giải thích chi tiết:   a)x^2+xy+4x+4y= x (x + y) + 4 (x + y)= (x + 4) (x + y)$  $ b)3xy+3x^2+7y+7x= 3x (y + x) + 7 (y + x)= (3x + 7) (y + x)$  $ c)x^2-4x+4-y&sup2;= (x - 2)^2 - y^2= (x - 2 + y) (x - 2 - y)$  $ d)xy-8y+x^2-8x= xy + x^2 - 8y - 8x= x (y + x) - 8 (y + x)= (x - 8) (y + x)$  $ e)4x^2-4x+x+1= 4x (x^2 - 1) + (x + 1)= 4x (x + 1) (x - 1) + (x + 1)$  $ = (x + 1) [4x (x - 1) + 1]= (x + 1) (4x^2 - 4x + 1)= (x + 1) (2x - 1)^2$  $ g)2xy+4z+8y+xz= 2xy + 8y + 4z + xz= 2y (x + 4) + z (4 + x)$  $ = 2y (x + 4) + z (x + 4)= (2y + z) (x + 4)$  $ h)y^2+10y+25-x^2= (y + 5)^2 - x^2= (y + 5 + x) (y + 5 - x)$  $ i)x^2-2^2-8x+16= x^2 - 8x + 16 - 2^2= (x - 4)^2 - 2^2$  $ = (x - 4 + 2) (x - 4 - 2)= (x - 2) (x - 6)$  $

khanhngantoan · Answer

a)x&sup2;+xy+4x+4y     = x (x + y) + 4 (x + y)     = (x + 4) (x + y)     b)3xy+3x&sup2;+7y+7x     = 3x (y + x) + 7 (y + x)     = (3x + 7) (y + x)     c)x&sup2;-4x+4-y&sup2;     = (x - 2)&sup2; - y&sup2;     = (x - 2 + y) (x - 2 - y)     d)xy-8y+x&sup2;-8x     = xy + x&sup2; - 8y - 8x     = x (y + x) - 8 (y + x)     = (x - 8) (y + x)     e)4x&sup3;-4x+x+1     = 4x (x&sup2; - 1) + (x + 1)     = 4x (x + 1) (x - 1) + (x + 1)     = (x + 1) [4x (x - 1) + 1]     = (x + 1) (4x&sup2; - 4x + 1)     = (x + 1) (2x - 1)&sup2;     g)2xy+4z+8y+xz      = 2xy + 8y + 4z + xz     = 2y (x + 4) + z (4 + x)     =   2y (x + 4) + z (x + 4)     = (2y + z) (x + 4)     h)y&sup2;+10y+25-x&sup2;     = (y + 5)&sup2; - x&sup2;     = (y + 5 + x) (y + 5 - x)    i)x&sup2;-2&sup2;-8x+16   = x&sup2; - 8x + 16 - 2&sup2;   = (x - 4)&sup2; - 2&sup2;   = (x - 4 + 2) (x - 4 - 2)   = (x - 2) (x - 6)