Question

Помогите разложить на множители

Answer 1

1) $x^2-2xy+y^2-z^2=(x-y)^2-z^2=[(x-y)-z]*[(x-y)+z]=$

$=(x-y-z)(x-y+z)$

2) $a^3-10a^2x-30ax^2+27x^3=a^3+27x^3-10a^2x-30ax^2=$

$=a^3+(3x)^3+(-10ax)*a+(-10ax)*3x=$

$=(a+3x)*[a^2-a*3x+(3x)^2]+(-10ax)*(a+3x)=$

$=(a+3x)*[a^2-a*3x+(3x)^2+(-10ax)]=$

$=(a+3x)*[a^2-3ax-10ax+9x^2] =(a+3x)(a^2-13ax+9x^2)$

3) $(a-3b)(a+2b)-3a(-a-2b)= (a-3b)(a+2b)+3a(a+2b)=$

$=[(a-3b)+3a]*(a+2b)=(4a-3b)(a+2b)$

4) $(64x^4y^2-9)^2-81= (64x^4y^2-9)^2-9^2=$

$=[(64x^4y^2-9)-9]*[(64x^4y^2-9)+9]=$

$=[64x^4y^2-18]*[64x^4y^2]=[2*32x^4y^2-2*9]*[64x^4y^2]=$

$=2*64x^4y^2*(32x^4y^2-9)=128x^4y^2(32x^4y^2-9)$

5) $2 frac{10}{27} a^6-16a^4+36a^2-27=frac{2*27+10}{27} a^6-16a^4+36a^2-27=$

$=frac{64}{27}*a^6-27-16a^4+36a^2= frac{64a^6-27^2}{27}-16a^4+36a^2=$

$= frac{(4a^2)^3-9^3}{27}+(-4a^2)*4a^2+(-4a^2)*(-9)=$

$=frac{1}{27}*[(4a^2)^3-9^3]+(-4a^2)*(4a^2+(-9))=$

$=frac{1}{27}*[4a^2-9]*[(4a^2)^2-4a^2*9+9^2]-4a^2*(4a^2-9)=$

$=frac{1}{27}*(16a^4-36a^2+81)*(4a^2-9)-4a^2*(4a^2-9)=$

$=[frac{1}{27}*(16a^4-36a^2+81)-4a^2]*(4a^2-9)=$

$=[frac{16a^4-36a^2+81-27*4a^2}{27}]*[(2a)^2-3^2]=$

$=[frac{16a^4-144a^2+81}{27}]*[(2a)-3]*[(2a)+3]=$

$=frac{16a^4-144a^2+81}{27}*(2a-3)(2a+3)$