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(ax+by)方+(bx-ay)方 (x-y)(x-y-3)+2 (x+1)(x+2)(x+3)(x+4)-24 因式分解(1)(ax+by)方+(bx-ay)方,,(2)(x-y)(x-y-3)+2 ,,(3)x+1)(x+2)(x+3)(x+4)-24

题目详情
(ax+by)方+(bx-ay)方 (x-y)(x-y-3)+2 (x+1)(x+2)(x+3)(x+4)-24 因式分解
(1)(ax+by)方+(bx-ay)方,,(2)(x-y)(x-y-3)+2 ,,(3)x+1)(x+2)(x+3)(x+4)-24
▼优质解答
答案和解析
(ax+by)^2+(bx-ay)^2=(ax)^2+(by)^2-2abxy+(bx)^2+(ay)^2-2abxy=(a^2+b^2)x^2+(a^2+b^2)y^2=(a^2+b^2)(x^2+y^2)
(x-y)(x-y-3)+2 =(x-y)^2-3(x-y)+2=[(x-y)-1][(x-y)-2]
(x+1)(x+2)(x+3)(x+4)-24=(x+1)(x+4)(x+2)(x+3)-24=(x^2+5x+4)(x^2+5x+4)=(x^2+5x)^2+10(x^2+5x)=(x^2+5x)(x^2+5x+10)