Đáp án + Giải thích các bước giải:
`a)` `x^2+10x+25`
`=x^2+2*x*5+5^2`
`=(x+5)^2`
`b)` `25x^2-20xy+4y^2`
`=(5x)^2-2*5x*2y+(2y)^2`
`=(5x-2y)^2`
`c)` `9x^4+24x^2+16`
`=(3x^2)^2+2*3x^2*4+4^2`
`=(3x^2+4)^2`
`d)` `x^3+8`
`=x^3+2^3`
`=(x+2)(x^2-2x+4)`
`e)` `8x^3+27y^3`
`=(2x)^3+(3y)^3`
`=(2x+3y)[(2x)^2-2x*3y+(3y)^2]`
`=(2x+3y)(4x^2-6xy+9y^2)`
`f)` `x^3-125`
`=x^3-5^3`
`=(x-5)(x^2+5x+25)`
`g)` `x^6-1`
Cách 1 :
`x^6-1=(x^3)^2-1^2`
`=(x^3-1)(x^3+1)`
`=(x-1)(x^2+x+1)(x+1)(x^2-x+1)`
Cách 2 :
`x^6-1=(x^2)^3-1^3`
`=(x^2-1)[(x^2)^2+x^2+1]`
`=(x^2-1)(x^4+x^2+1)`
`=(x-1)(x+1)(x^4+x^2+1)`
`=(x-1)(x+1)(x^4+x+x^2-x+1)`
`=(x-1)(x+1)[x(x^3+1)+(x^2-x+1)]`
`=(x-1)(x+1)[x(x+1)(x^2-x+1)+(x^2-x+1)]`
`=(x-1)(x+1)(x^2-x+1)[x(x+1)+1]`
`=(x-1)(x+1)(x^2-x+1)(x^2+x+1)`
`h)` `x^3+15x^2+75x+125`
`=x^3+3*x^2*5+3*x*5^2+5^3=(x+5)^3`
VD3 :
`a)` `x^2+4x+3`
`=x^2+x+3x+3`
`=x(x+1)+3(x+1)=(x+1)(x+3)`
`b)` `8x^3-36x^2+54x-26`
`=[(2x)^3-3*(2x)^2*3+3*2x*3^2-3^3]+1`
`=(2x-3)^3+1`
`=(2x-3)^3+1^3`
`=(2x-3+1)[(2x-3)^2+(2x-3)+1]`
`=(2x-2)(4x^2-12x+9+2x-3+1)`
`=(2x-2)(4x^2-10x+7)`.
