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

$$x^{3}-27x^{2}+199x-5$$

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}.

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

Naqqas 32 minn 49 biex tikseb 17.

$$\left(x-13\right)\left(x^{2}-14x+17\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x-13 b'kull terminu ta' x^{2}-14x+17.

$$x^{3}-14x^{2}+17x-13x^{2}+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+17x+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 17x u 182x biex tikseb 199x.

$$x^{3}-27x^{2}+199x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+199x-221+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

Żid 14 u 40 biex tikseb 54.

$$x^{3}-27x^{2}+199x-221+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+199x-221-10x+270+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 199x u -10x biex tikseb 189x.

$$x^{3}-27x^{2}+189x-221+270+2\left(8+5\left(x-7\right)\right)$$

Żid -221 u 270 biex tikseb 49.

$$x^{3}-27x^{2}+189x+49+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+189x+49+2\left(8+5x-35\right)$$

Naqqas 35 minn 8 biex tikseb -27.

$$x^{3}-27x^{2}+189x+49+2\left(-27+5x\right)$$

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

$$x^{3}-27x^{2}+189x+49-54+10x$$

Naqqas 54 minn 49 biex tikseb -5.

$$x^{3}-27x^{2}+189x-5+10x$$

Ikkombina 189x u 10x biex tikseb 199x.

$$x^{3}-27x^{2}+199x-5$$

Espandi

$$x^{3}-27x^{2}+199x-5$$

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}.

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

Naqqas 32 minn 49 biex tikseb 17.

$$\left(x-13\right)\left(x^{2}-14x+17\right)+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' x-13 b'kull terminu ta' x^{2}-14x+17.

$$x^{3}-14x^{2}+17x-13x^{2}+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+17x+182x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 17x u 182x biex tikseb 199x.

$$x^{3}-27x^{2}+199x-221+5\left(-2\left(x-7\right)+40\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+199x-221+5\left(-2x+14+40\right)+2\left(8+5\left(x-7\right)\right)$$

Żid 14 u 40 biex tikseb 54.

$$x^{3}-27x^{2}+199x-221+5\left(-2x+54\right)+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+199x-221-10x+270+2\left(8+5\left(x-7\right)\right)$$

Ikkombina 199x u -10x biex tikseb 189x.

$$x^{3}-27x^{2}+189x-221+270+2\left(8+5\left(x-7\right)\right)$$

Żid -221 u 270 biex tikseb 49.

$$x^{3}-27x^{2}+189x+49+2\left(8+5\left(x-7\right)\right)$$

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

$$x^{3}-27x^{2}+189x+49+2\left(8+5x-35\right)$$

Naqqas 35 minn 8 biex tikseb -27.

$$x^{3}-27x^{2}+189x+49+2\left(-27+5x\right)$$

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

$$x^{3}-27x^{2}+189x+49-54+10x$$

Naqqas 54 minn 49 biex tikseb -5.

$$x^{3}-27x^{2}+189x-5+10x$$

Ikkombina 189x u 10x biex tikseb 199x.

$$x^{3}-27x^{2}+199x-5$$