Resposta:

10)

(a-b)³=a³-3a²b+3ab²-b³

(a-b)³=a³-b³-3ab(a-b)

a³-b³=(a-b)³+3ab(a-b)

a³-b³=(a-b)*[(a-b)²+3ab]

a³-b³=(a-b)*[a²-2ab+b²+3ab]

a³-b³=(a-b)*[a²+ab+b²]

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(a+b)³=a³+3a²b+3ab²+b³

(a-b)³=a³+b³+3ab(a+b)

a³+b³=(a+b)³3ab(a+b)

a³-b³=(a+b)*[(a-b)²3ab]

a³+b³=(a+b)*[a²+2ab+b²-3ab]

a³+b³=(a+b)*[a²-ab+b²]

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x²-y²=(x-y)*(x-y)

a)

8x³-y³=(2x)³-y³

(2x)³-y³=(2x-y)*[(2x)²+(2x)*y+(-y)²]

(2x)³-y³=(2x-y)*[4x²+2yx+y²]

8x³-y³=(2x-y)*[4x²+2yx+y²]

b)

27a³+1=(3a)³+1=(3a+1)*[(3a)²-1*3a+1²]

27a³+1=(3a+1)*(9a²-a+1)

c)

x³-27y³=x³-(3y)³=(x-3y)*[x²+x*3y+(3y)²]

x³-27y³=(x-3y)*[x²+3xy+9y²

11.

a)

3x²-6x+3=3x²-3x - 3x +3 =3x(x-1)-3(x-1)

=(x-1)*(3x-1)

b)

x³y+y=y*(x³+1)=y*(x+1)*(x²-x+1)

c)

ax²-a+bx²-b=a*(x²-1)+b*(x²-1)

=(x²-1)*(a+b)

=(x+1)*(x-1)*(a+b)