Đáp án:
`a)(5y+1)^2`
`b)x^2(x-2)^2`
`c)x(x+5)(x^2+5x+10)`
Giải thích các bước giải:
`a)`Sửa đề:`25y^2+10y^8+1`
`→25y^2+10y+1`
`25y^2+10y+1`
`=(5y)^2+2.5y.1+1^2`
`=(5y+1)^2`
`b)(x-1)^4-2(x^2-2x+1)+1`
`=(x-1)^4-2(x-1)^2+1`
`=[(x-1)^2]^2-2.(x-1)^2 .1+1^2`
`=[(x-1)^2-1]^2`
`=[(x-1+1)(x-1-1)]^2`
`=[x(x-2)]^2`
`=x^2(x-2)^2`
`c)(x+1)(x+2)(x+3)(x+4)-24`
`=[(x+1)(x+4)][(x+2)(x+3)]-24`
`=(x^2+4x+x+4)(x^2+3x+2x+6)-24`
`=(x^2+5x+4)(x^2+5x+6)-24`
Đặt `x^2+5x+5=a` khi đó ta được:
`(a-1)(a+1)-24`
`=a^2-1-24`
`=a^2-25`
`=a^2-5^2`
`=(a-5)(a+5)`
`=(x^2+5x+5-5)(x^2+5x+5+5)`
`=(x^2+5x)(x^2+5x+10)`
`=x(x+5)(x^2+5x+10)`
