Đáp án `+` Giải thích các bước giải `!`
`44.`
`64(3x-1)^3-125(1+2x)^3`
`= [4(3x-1)]^3-[5(1+2x)]^3`
`= (12x-4)^3-(5+10x)^3`
`= [(12x-4)-(5+10x)][(12x-4)^2+(12x-4)(5+10x)+(5+10x)^2]`
`= (12x-4-5-10x)(144x^2-96x+16+60x+120x^2-20-40x+25+100x+100x^2)`
`= (2x-9)[(144x^2+120x^2+100x^2)+(-96x+60x-40x+100x)+(16-20+25)]`
`= (2x-9)(364x^2+24x+21)`
`= 728x^3+48x^2+42x-3276x^2-216x-189`
`= 728x^3+(48x^2-3276x^2)+(42x-216x)-189`
`= 728x^3-3228x^2-174x-189`
`45.`
`27(2x-1)^3-8(1-x)^3`
`= [3(2x-1)]^3-[2(1-x)]^3`
`= (6x-3)^3-(2-2x)^3`
`= [(6x-3)-(2-2x)][(6x-3)^2+(6x-3)(2-2x)+(2-2x)^2]`
`= (6x-3-2+2x)(36x^2-36x+9+12x-12x^2-6+6x+4-8x+4x^2)`
`= (8x-5)[(36x^2-12x^2+4x^2)+(-36x+12x+6x-8x)+(9-6+4)]`
`= (8x-5)(28x^2-26x+7)`
`= 224x^3-208x^2+56x-140x^2+130x-35`
`= 224x^3+(-208x^2-140x^2)+(56x+130x)-35`
`= 224x^3-348x^2+186x-35`
Áp dụng:
`+)` `a^3-b^3 = (a-b)(a^2+ab+b^2)`
`+)` `(a+b)^2 = a^2+2ab+b^2`
`+)` `(a-b)^2 = a^2-2ab+b^2`
