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

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

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}.

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

Tangohia te 32 i te 49, ka 17.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-13 ki ia tau o x^{2}-14x+17.

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

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

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

Pahekotia te 17x me 182x, ka 199x.

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

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

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

Tāpirihia te 14 ki te 40, ka 54.

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

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

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

Pahekotia te 199x me -10x, ka 189x.

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

Tāpirihia te -221 ki te 270, ka 49.

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

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

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

Tangohia te 35 i te 8, ka -27.

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

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

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

Tangohia te 54 i te 49, ka -5.

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

Pahekotia te 189x me 10x, ka 199x.

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

Whakaroha

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

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}.

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

Tangohia te 32 i te 49, ka 17.

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

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-13 ki ia tau o x^{2}-14x+17.

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

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

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

Pahekotia te 17x me 182x, ka 199x.

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

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

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

Tāpirihia te 14 ki te 40, ka 54.

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

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

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

Pahekotia te 199x me -10x, ka 189x.

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

Tāpirihia te -221 ki te 270, ka 49.

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

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

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

Tangohia te 35 i te 8, ka -27.

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

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

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

Tangohia te 54 i te 49, ka -5.

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

Pahekotia te 189x me 10x, ka 199x.

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