Đáp án + Giải thích các bước giải:
`37.` `1+1/64x^3`
`=1^3+(1/4x)^3`
`=(1+1/4x)[1^2-1/4x+(1/4x)^2]`
`=(1+1/4x)(1-1/4x+1/16x^2)`
`38.` `1-q^3`
`=1^3-q^3`
`=(1-q)(1+q+q^2)`
`39.` `64x^3+1/8`
`=(4x)^3+(1/2)^3`
`=(4x+1/2)[(4x)^2-4x*1/2+(1/2)^2]`
`=(4x+1/2)(16x^2-2x+1/4)`
`40.` `27b^3-8a^3`
`=(3b)^3-(2a)^3`
`=(3b-2a)[(3b)^2+3b*2a+(2a)^2]`
`=(3b-2a)(9b^2+6ba+4a^2)`
`41.` `1/8a^3b^9+64x^3`
`=(1/2ab^3)^3+(4x)^3`
`=(1/2ab^3+4x)[(1/2ab^3)^2-1/2ab^3*4x+(4x)^2]`
`=(1/2ab^3+4x)(1/4a^2b^6-2ab^3x+16x^2)`
`42.` `x^4-64x`
`=x(x^3-64)`
`=x(x^3-8^3)`
`=x(x-8)(x^2+8x+64)`
`43.` `x^6-x^2`
`=x^2(x^4-1)`
`=x^2(x^2-1)(x^2+1)`
`=x^2(x-1)(x+1)(x^2+1)`
`44.` `8x^3+27y^3`
`=(2x)^3+(3y)^3`
`=(2x+3y)[(2x)^2-2x*3y+(3y)^2]`
`=(2x+3y)(4x^2-6xy+9y^2)`
`45.` `-1/125m^3-1/8p^3q^3`
`=(-1/5m)^3-(1/2pq)^3`
`=(-1/5m-1/2pq)[(-1/5m)^2+(-1/5m)*1/2pq+(1/2pq)^2]`
`=(-1/5m-1/2pq)(1/25m^2-1/10mpq+1/4p^2q^2)`
`46.` `64x^6-27y^6`
`=(4x^2)^3-(3y^2)^3`
`=(4x^2-3y^2)[(4x^2)^2+4x^2*3y^2+(3y^2)^2]`
`=(4x^2-3y^2)(16x^4+12x^2y^2+9y^4)`
`47.` `-q^3+12q^2x-48qx^2+64x^3`
`=-(q^3-12q^2x+48qx^2-64x^3)`
`=-[q^3-3*q^2*4x+3*q*(4x)^2-(4x)^3]`
`=-(q-4x)^3`
`48.` `a^3b^2+18a^2b^2+108ab^2+216b^2`
`=b^2(a^3+18a^2+108a+216)`
`=b^2(a^3+3*a^2*6+3*a*6^2+6^3)`
`=b^2(a+6)^3`.
