4.2

445

$\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$

a)

$\left(x+1\right)^3=x^3+3x^2+3x+1$

b)

$\left(x+2\right)^3=x^3+6x^2+12x+8$

c)

$\left(x-3\right)^3=x^3-9x^2+27x-27$

d)

$\left(x+10\right)^3=x^3+30x^2+300x+1000$

435

a)

$\left(x-1\right)\left(x+1\right)\left(2x-3\right)=\left(x^2+1\right)\left(2x-3\right)=2x^2-3x^2+2x-3=-x^2+2x-3$

b)

$\left(2x+1\right)\left(3x-1\right)\left(x+2\right)=\left(6x^2-x-1\right)\left(x+2\right)=6x^3-x^2-x+12x^2-2x-2=6x^3+11x^2-3x-2$

432

a)
$\left(x^2-1\right)\left(x^2+1\right)$
$laskukaava\ \left(a+b\right)\left(a-b\right)=a^2-b^2$

$\left(x^2\right)^2-1^2=x^4-1$

b)

$\left(2x^3+1\right)^2$
$laskukaava\ \left(a+b\right)^2=a^2+2ab+b^2$
$\left(2x^3\right)^2+4x^3+1^2=4x^6+4x^3+1$

c)

$\left(x^4-1\right)^2$
$laskukaava\ \left(a-b\right)^2=a^2-2ab+b^2$
$\left(x^4\right)^2-2x^4+1^2=x^8-2x^4+1$

431

$\left(x^2\right)^3=x^6$
$\left(3x\right)^2=9x^2$
$\left(-2x^4\right)^3=8x^{12}$
$\left(-x^3\right)^4=x^{12}$