Issolvi (x-13)((x-7)(x-7)+32)+5(-2(x-7)+40)+2(8+5(x-7))

$$( x - 13 ) ( ( x - 7 ) ( x - 7 ) + 32 ) + 5 ( - 2 ( x - 7 ) + 40 ) + 2 ( 8 + 5 ( x - 7 ) )$$

Evalwa

$$x^{3}-27x^{2}+263x-837$$

Passi tas-Soluzzjonijiet

Immultiplika x-7 u x-7 biex tikseb \left(x-7\right)^{2}.

$$\left(x-13\right)\left(\left(x-7\right)^{2}+32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-7\right)^{2}.

$$\left(x-13\right)\left(x^{2}-14x+49+32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Żid 49 u 32 biex tikseb 81.

$$\left(x-13\right)\left(x^{2}-14x+81\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x-13 b'kull terminu ta' x^{2}-14x+81.

$$x^{3}-14x^{2}+81x-13x^{2}+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Ikkombina -14x^{2} u -13x^{2} biex tikseb -27x^{2}.

$$x^{3}-27x^{2}+81x+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 81x u 182x biex tikseb 263x.

$$x^{3}-27x^{2}+263x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika -2 b'x-7.

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

Żid 14 u 40 biex tikseb 54.

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika 5 b'-2x+54.

$$x^{3}-27x^{2}+263x-1053-10x+270+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 263x u -10x biex tikseb 253x.

$$x^{3}-27x^{2}+253x-1053+270+2\left(8+5\left(x-7\right)\right)$$

Żid -1053 u 270 biex tikseb -783.

$$x^{3}-27x^{2}+253x-783+2\left(8+5\left(x-7\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika 5 b'x-7.

$$x^{3}-27x^{2}+253x-783+2\left(8+5x-35\right)$$

Naqqas 35 minn 8 biex tikseb -27.

$$x^{3}-27x^{2}+253x-783+2\left(-27+5x\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'-27+5x.

$$x^{3}-27x^{2}+253x-783-54+10x$$

Naqqas 54 minn -783 biex tikseb -837.

$$x^{3}-27x^{2}+253x-837+10x$$

Ikkombina 253x u 10x biex tikseb 263x.

$$x^{3}-27x^{2}+263x-837$$

Espandi

$$x^{3}-27x^{2}+263x-837$$

Passi tas-Soluzzjonijiet

Immultiplika x-7 u x-7 biex tikseb \left(x-7\right)^{2}.

$$\left(x-13\right)\left(\left(x-7\right)^{2}+32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-7\right)^{2}.

$$\left(x-13\right)\left(x^{2}-14x+49+32\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Żid 49 u 32 biex tikseb 81.

$$\left(x-13\right)\left(x^{2}-14x+81\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x-13 b'kull terminu ta' x^{2}-14x+81.

$$x^{3}-14x^{2}+81x-13x^{2}+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Ikkombina -14x^{2} u -13x^{2} biex tikseb -27x^{2}.

$$x^{3}-27x^{2}+81x+182x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 81x u 182x biex tikseb 263x.

$$x^{3}-27x^{2}+263x-1053+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika -2 b'x-7.

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

Żid 14 u 40 biex tikseb 54.

$$x^{3}-27x^{2}+263x-1053+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika 5 b'-2x+54.

$$x^{3}-27x^{2}+263x-1053-10x+270+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 263x u -10x biex tikseb 253x.

$$x^{3}-27x^{2}+253x-1053+270+2\left(8+5\left(x-7\right)\right)$$

Żid -1053 u 270 biex tikseb -783.

$$x^{3}-27x^{2}+253x-783+2\left(8+5\left(x-7\right)\right)$$

Uża l-propjetà distributtiva biex timmultiplika 5 b'x-7.

$$x^{3}-27x^{2}+253x-783+2\left(8+5x-35\right)$$

Naqqas 35 minn 8 biex tikseb -27.

$$x^{3}-27x^{2}+253x-783+2\left(-27+5x\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'-27+5x.

$$x^{3}-27x^{2}+253x-783-54+10x$$

Naqqas 54 minn -783 biex tikseb -837.

$$x^{3}-27x^{2}+253x-837+10x$$

Ikkombina 253x u 10x biex tikseb 263x.

$$x^{3}-27x^{2}+263x-837$$