Issolvi (x-1)^2(x+2)(x^2+x+1)^2

$$( x - 1 ) ^ { 2 } ( x + 2 ) ( x ^ { 2 } + x + 1 ) ^ { 2 }$$

Evalwa

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

$$\left(x^{2}-2x+1\right)\left(x+2\right)\left(x^{2}+x+1\right)^{2}$$

Ikkwadra x^{2}+x+1.

$$\left(x^{2}-2x+1\right)\left(x+2\right)\left(x^{4}+2x^{3}+3x^{2}+2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}-2x+1 b'x+2 u kkombina termini simili.

$$\left(x^{3}-3x+2\right)\left(x^{4}+2x^{3}+3x^{2}+2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{3}-3x+2 b'x^{4}+2x^{3}+3x^{2}+2x+1 u kkombina termini simili.

$$x^{7}+2x^{6}-2x^{4}-4x^{3}+x+2$$

Espandi

$$x^{7}+2x^{6}-2x^{4}-4x^{3}+x+2$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

$$\left(x^{2}-2x+1\right)\left(x+2\right)\left(x^{2}+x+1\right)^{2}$$

Ikkwadra x^{2}+x+1.

$$\left(x^{2}-2x+1\right)\left(x+2\right)\left(x^{4}+2x^{3}+3x^{2}+2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}-2x+1 b'x+2 u kkombina termini simili.

$$\left(x^{3}-3x+2\right)\left(x^{4}+2x^{3}+3x^{2}+2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{3}-3x+2 b'x^{4}+2x^{3}+3x^{2}+2x+1 u kkombina termini simili.

$$x^{7}+2x^{6}-2x^{4}-4x^{3}+x+2$$