Whakaoti i te a^{2}x^{3}-x^{3}b^{2}-a^2y^3+y^3b^2=

$$a ^ { 2 } x ^ { 3 } - x ^ { 3 } b ^ { 2 } - a ^ { 2 } y ^ { 3 } + y ^ { 3 } b ^ { 2 } =$$

Tauwehe

$$\left(a-b\right)\left(x-y\right)\left(a+b\right)\left(x^{2}+xy+y^{2}\right)$$

Ngā Upane Otinga

Mahia te whakarōpūtanga a^{2}x^{3}-x^{3}b^{2}-a^{2}y^{3}+y^{3}b^{2}=\left(a^{2}x^{3}-x^{3}b^{2}\right)+\left(-a^{2}y^{3}+y^{3}b^{2}\right), ka whakatauwehea atu x^{3} i te tuatahi me -y^{3} i te rōpū tuarua.

$$x^{3}\left(a^{2}-b^{2}\right)-y^{3}\left(a^{2}-b^{2}\right)$$

Whakatauwehea atu te kīanga pātahi a^{2}-b^{2} mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a^{2}-b^{2}\right)\left(x^{3}-y^{3}\right)$$

Whakaarohia te a^{2}-b^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

$$\left(a-b\right)\left(a+b\right)$$

Whakaarohia te x^{3}-y^{3}. Ka taea te rerekētanga o ngā pūtoru te whakatauwehe mā te whakamahi i te ture: p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right).

$$\left(x-y\right)\left(x^{2}+xy+y^{2}\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(a-b\right)\left(a+b\right)\left(x-y\right)\left(x^{2}+xy+y^{2}\right)$$

Aromātai

$$\left(a^{2}-b^{2}\right)\left(x^{3}-y^{3}\right)$$