Whakaoti i te (x-13)((x-7)(x-7)+32)+5(-2(x-7)+40)+2(8+5(x-7))

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

Aromātai

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

Ngā Upane Otinga

Whakareatia te x-7 ki te x-7, ka \left(x-7\right)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-7\right)^{2}.

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

Tāpirihia te 49 ki te 32, ka 81.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-13 ki ia tau o x^{2}-14x+81.

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

Pahekotia te -14x^{2} me -13x^{2}, ka -27x^{2}.

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

Pahekotia te 81x me 182x, ka 263x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x-7.

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

Tāpirihia te 14 ki te 40, ka 54.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te -2x+54.

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

Pahekotia te 263x me -10x, ka 253x.

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

Tāpirihia te -1053 ki te 270, ka -783.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x-7.

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

Tangohia te 35 i te 8, ka -27.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te -27+5x.

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

Tangohia te 54 i te -783, ka -837.

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

Pahekotia te 253x me 10x, ka 263x.

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

Whakaroha

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

Ngā Upane Otinga

Whakareatia te x-7 ki te x-7, ka \left(x-7\right)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-7\right)^{2}.

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

Tāpirihia te 49 ki te 32, ka 81.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-13 ki ia tau o x^{2}-14x+81.

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

Pahekotia te -14x^{2} me -13x^{2}, ka -27x^{2}.

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

Pahekotia te 81x me 182x, ka 263x.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x-7.

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

Tāpirihia te 14 ki te 40, ka 54.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te -2x+54.

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

Pahekotia te 263x me -10x, ka 253x.

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

Tāpirihia te -1053 ki te 270, ka -783.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5 ki te x-7.

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

Tangohia te 35 i te 8, ka -27.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te -27+5x.

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

Tangohia te 54 i te -783, ka -837.

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

Pahekotia te 253x me 10x, ka 263x.

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