Đáp án+Giải thích các bước giải:
`5)`
`a)` `(x^2-2x+2)(x^2-2)(x^2+2x+2)(x^2+2)`
`=[(x^2+2-2x)(x^2+2+2x)][(x^2-2)(x^2+2)]`
`=[(x^2+2)^2-(2x)^2][(x^2)^2-2^2]`
`=[(x^4+2.2x^2+2^2)-4x^2](x^4-4)`
`=(x^4+4x^2+4-4x^2)(x^4-4)`
`=[x^4+4+(4x^2-4x^2)](x^4-4)`
`=(x^4+4)(x^4-4)`
`=(x^4)^2-4^2`
`=x^8-16`
`b)` `(x+2)(x^2-2x+4)-(x-1)(x^2+x+1)`
`=(x+2)(x^2-2.x+2^2)-(x-1)(x^2+x.1+1^2)`
`=x^3+2^3-(x^3-1^3)`
`=x^3+8-x^3+1`
`=(x^3-x^3)+(8+1)`
`=9`
`c)` `(1/3a^2-1/2b)(1/3a^2+1/2b)-(a+1/2b)(a^2-1/2ab+1/4b^2)`
`=(1/3a^2)^2-(1/2b)^2-(a+1/2b)[a^2-a.{1}/2b+(1/2b)^2]`
`=1/9a^4-1/4b^2-[a^3+(1/2b)^3]`
`=1/9a^4-1/4b^2-a^3-1/8b^3`
`=a^4/9-b^2/4-a^3-b^3/8`
`6)`
`a)` `(4x-6)^2-16(3-x)^2`
`=(4x)^2-2.4x.6+6^2-16(3^2-2.3.x+x^2)`
`=16x^2-48x+36-16(9-6x+x^2)`
`=16x^2-48x+36-16.9+16.6x-16x^2`
`=16x^2-48x+36-144+96x-16x^2`
`=(16x^2-16x^2)+(96x-48x)+(36-144)`
`=48x-108`
Thay `x=-7` vào, ta được:
`48.(-7)-108=-336-108=-444`
`b)` `(x-1)(x^2+x+1)+(x+3)(x^2-3x+9)`
`=(x-1)(x^2+x.1+1^2)+(x+3)(x^2-3.x+3^2)`
`=x^3-1^3+x^3-3^3`
`=x^3-1+x^3+27`
`=(x^3+x^3)+(27-1)`
`=2x^3+26`
Thay `x=-1` vào, ta dược:
`2(-1)^3+26=2(-1)+26=-2+26=24`
`c)` `(2x+7)(4x^2-14x+49)-8x(x-2)^2`
`=(2x+7)[(2x)^2-2x.7+7^2]-8x(x^2-4x+4)`
`=(2x)^3+7^3-8x.x^2+8x.4x-8x.4`
`=8x^3+343-8x^3+32x^2-32x`
`=(8x^3-8x^3)+32x^2-32x+343`
`=32x^2-32x+343`
Thay `x=3` vào, ta được:
`32.3^2-32.3+343=32.9-32.3+343=288-96+343=535`
