Bài 7:
`a)x^4+4x²+4`
`=(x²)^2+2.x².2+2²`
`=(x²+2)²`
`9a^4+24a²b²+16b^4`
`=(3a²)^2+2.3a².4b²+(4b²)^2`
`=(3a²+4b²)²`
`b)4a²b²-c²d²`
`=(2ab)²-(cd)²`
`=(2ab+cd)(2ab-cd)`
`a³+27`
`=a³+3³`
`=(a+3)(a²-3a+9)`
`x^16-y^16`
`=(x^8)^2-(y^8)^2`
`=(x^8+y^8)(x^8-y^8)`
`=(x^8+y^8)[(x^4)^2-(y^4)^2]`
`=(x^8+y^8)(x^4+y^4)(x^4-y^4)`
`=(x^8+y^8)(x^4+y^4)[(x^2)^2-(y^2)^2]`
`=(x^8+y^8)(x^4+y^4)(x²+y²)(x²-y²)`
`=(x^8+y^8)(x^4+y^4)(x²+y²)(x+y)(x-y)`
`c)x³-125`
`=x³-5³`
`=(x-5)(x³+5x+25)`
`-64+1/8x³`
`=1/8x³-64`
`=(1/2x)^3-4³`
`=(1/2x-4)(1/4x+2x+16)`
`d)8x³+60x²y+150xy²+125y³`
`=(2x)³+3.(2x)².5y+3.2x.(5y)²+(5y)³`
`=(2x+5y)³`
Bài 8:
`a)9x²+30x+25`
`=(3x)²+2.3x.5+5²`
`=(3x+5)²`
`4/9x^4-16x²`
`=(2/3x²)^2-(4x)²`
`=(2/3x²+4x)(2/3x²-4x)`
`b)12/5x²y²-9x^4-4/25y^4`
`=-(9x^4-12/5x²y²+4/25y^4)`
`=-[(3x²)^2-2.3x². 2/5y²+(2/5y²)^2]`
`=-(3x²-2/5y²)^2`
`c)a²y²+b²x²-2axby`
`=a²y²-2axby+b²x²`
`=(ay)²-2.ay.bc+(bx)²`
`=(ay-bx)²`
`d)` Sửa đề `64x²-8a+b²`
`→64x²-(8a+b)²`
`64x²-(8a+b)²`
`=(8x)²-(8a+b)²`
`=(8x+8a+b)(8x-8a-b)`
`e)` Sửa đề:`100-3x-y²`
`→100-(3x-y)²`
`100-(3x-y)²`
`=10²-(3x-y)²`
`=(10+3x-y)(10-3x+y)`
`g)27x³-a³b³`
`=(3x)²-(ab)³`
`=(3x-ab)(9x²+3xab+a²b²)`
Bài 9:
`a)27x³-27x²+3x+1`
`=27x³-9x²-18x²+6x-3x+1`
`=(27x³-9x²)-(18x²-6x)-(3x-1)`
`=9x²(3x-1)-6x(3x-1)-(3x-1)`
`=(3x-1)(9x²-6x-1)`
`b)x³-3x²+3x-1`
`=x³-3.x².1+3.x.1²-1³`
`=(x-1)³`
`c)1/27+x³`
`=(1/3)^3+x³`
`=(1/3+x)[(1/3)^2+1/3 .x+x²]`
`=(1/3+x)(1/9+1/3x+x²)`
`d)0,001-1000x³`
`=(0,1)^3-(10x)³`
`=(0,1-10x)[(0,01)²+0,01.10x+(10x)²]`
`=(0,1-10x)(0,01+x+100x²)`
