Issolvi f(x)=-(x-2)(x+1)^2(x-3)^2

$$f ( x ) = - ( x - 2 ) ( x + 1 ) ^ { 2 } ( x - 3 ) ^ { 2 }$$

Evalwa

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

Passi tas-Soluzzjonijiet

Biex issib l-oppost ta' x-2, sib l-oppost ta' kull terminu.

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

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

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-3\right)^{2}.

$$\left(-x+2\right)\left(x^{2}+2x+1\right)\left(x^{2}-6x+9\right)$$

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

$$\left(-x^{3}+3x+2\right)\left(x^{2}-6x+9\right)$$

Uża l-propjetà distributtiva biex timmultiplika -x^{3}+3x+2 b'x^{2}-6x+9 u kkombina termini simili.

$$-x^{5}+6x^{4}-6x^{3}-16x^{2}+15x+18$$

Espandi

$$18+15x-16x^{2}-6x^{3}+6x^{4}-x^{5}$$

Passi tas-Soluzzjonijiet

Biex issib l-oppost ta' x-2, sib l-oppost ta' kull terminu.

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

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

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-3\right)^{2}.

$$\left(-x+2\right)\left(x^{2}+2x+1\right)\left(x^{2}-6x+9\right)$$

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

$$\left(-x^{3}+3x+2\right)\left(x^{2}-6x+9\right)$$

Uża l-propjetà distributtiva biex timmultiplika -x^{3}+3x+2 b'x^{2}-6x+9 u kkombina termini simili.

$$-x^{5}+6x^{4}-6x^{3}-16x^{2}+15x+18$$