Whakaoti i te 48m^2-40m-18m+15

$$48 m ^ { 2 } - 40 m - 18 m + 15$$

Tauwehe

$$\left(6m-5\right)\left(8m-3\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$48m^{2}-58m+15$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 48m^{2}+am+bm+15. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-58 ab=48\times 15=720$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 720.

$$-1,-720 -2,-360 -3,-240 -4,-180 -5,-144 -6,-120 -8,-90 -9,-80 -10,-72 -12,-60 -15,-48 -16,-45 -18,-40 -20,-36 -24,-30$$

Tātaihia te tapeke mō ia takirua.

$$-1-720=-721 -2-360=-362 -3-240=-243 -4-180=-184 -5-144=-149 -6-120=-126 -8-90=-98 -9-80=-89 -10-72=-82 -12-60=-72 -15-48=-63 -16-45=-61 -18-40=-58 -20-36=-56 -24-30=-54$$

Ko te otinga te takirua ka hoatu i te tapeke -58.

$$a=-40 b=-18$$

Tuhia anō te 48m^{2}-58m+15 hei \left(48m^{2}-40m\right)+\left(-18m+15\right).

$$\left(48m^{2}-40m\right)+\left(-18m+15\right)$$

Tauwehea te 8m i te tuatahi me te -3 i te rōpū tuarua.

$$8m\left(6m-5\right)-3\left(6m-5\right)$$

Whakatauwehea atu te kīanga pātahi 6m-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(6m-5\right)\left(8m-3\right)$$

Aromātai

$$\left(6m-5\right)\left(8m-3\right)$$

Ngā Upane Otinga

Pahekotia te -40m me -18m, ka -58m.

$$48m^{2}-58m+15$$