Đáp án + Giải thích các bước giải:
`1,(x-2)^2 -(x+2)^2 = x^2 - 4x + 4 - x^2 -4x -4 = -8x`
`2,(x-2y)^2 + (2x+y)^2 = x^2 - 4xy + 4y^2 + 4x^2 +4xy +y^2 = 5x^2 + 5y^2`
`3, (x+1)^2 - (x+2)(x-2) = x^2 +2x+1-x^2 + 4 = 2x + 5`
`4, (5+x)(5-x) - (x-5)^2 = 25-x^2 - x^2 +10x -25 = -2x^2 +10`
`5, (x-1)(x-3)-(x+10)(x-10) = x^2 -3x-x+3-x^2+10^2=-4x+3+100=-4x+103`
`6, (a^2+3)(3-a^2) - a^2(2021-a^2 = (3+a^2)(3-a^2) - 2021a^2 + a^4`
`=9 - a^4 -2021a^2+a^4 = 9-2021a^2`
`7, (x+2)(x^2-2x+4)-(x-3)(x^2+3x+9) = x^3 + 8 - x^3 + 27 =35`
Áp dụng :
`+) A^2+-2AB+B^2=(A+-B)^2 `
`+) A^2 - B^2=(A+B)(A-B)`
`+) A^3 +- B^3 = (A+-B)(A^2+-AB+B^2)`
