Whakaoti i te (4a-5b)(4a+5b)-(4a+2b)(4a-3b)+(-5b)^2

$$( 4 a - 5 b ) ( 4 a + 5 b ) - ( 4 a + 2 b ) ( 4 a - 3 b ) + ( - 5 b ) ^ { 2 }$$

Aromātai

$$2b\left(2a+3b\right)$$

Ngā Upane Otinga

Whakaarohia te \left(4a-5b\right)\left(4a+5b\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4a\right)^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Whakarohaina te \left(4a\right)^{2}.

$$4^{2}a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Whakarohaina te \left(5b\right)^{2}.

$$16a^{2}-5^{2}b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$16a^{2}-25b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4a+2b ki te 4a-3b ka whakakotahi i ngā kupu rite.

$$16a^{2}-25b^{2}-\left(16a^{2}-4ab-6b^{2}\right)+\left(-5b\right)^{2}$$

Hei kimi i te tauaro o 16a^{2}-4ab-6b^{2}, kimihia te tauaro o ia taurangi.

$$16a^{2}-25b^{2}-16a^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Pahekotia te 16a^{2} me -16a^{2}, ka 0.

$$-25b^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Pahekotia te -25b^{2} me 6b^{2}, ka -19b^{2}.

$$-19b^{2}+4ab+\left(-5b\right)^{2}$$

Whakarohaina te \left(-5b\right)^{2}.

$$-19b^{2}+4ab+\left(-5\right)^{2}b^{2}$$

Tātaihia te -5 mā te pū o 2, kia riro ko 25.

$$-19b^{2}+4ab+25b^{2}$$

Pahekotia te -19b^{2} me 25b^{2}, ka 6b^{2}.

$$6b^{2}+4ab$$

Whakaroha

$$4ab+6b^{2}$$

Ngā Upane Otinga

Whakaarohia te \left(4a-5b\right)\left(4a+5b\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(4a\right)^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Whakarohaina te \left(4a\right)^{2}.

$$4^{2}a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16a^{2}-\left(5b\right)^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Whakarohaina te \left(5b\right)^{2}.

$$16a^{2}-5^{2}b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$16a^{2}-25b^{2}-\left(4a+2b\right)\left(4a-3b\right)+\left(-5b\right)^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4a+2b ki te 4a-3b ka whakakotahi i ngā kupu rite.

$$16a^{2}-25b^{2}-\left(16a^{2}-4ab-6b^{2}\right)+\left(-5b\right)^{2}$$

Hei kimi i te tauaro o 16a^{2}-4ab-6b^{2}, kimihia te tauaro o ia taurangi.

$$16a^{2}-25b^{2}-16a^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Pahekotia te 16a^{2} me -16a^{2}, ka 0.

$$-25b^{2}+4ab+6b^{2}+\left(-5b\right)^{2}$$

Pahekotia te -25b^{2} me 6b^{2}, ka -19b^{2}.

$$-19b^{2}+4ab+\left(-5b\right)^{2}$$

Whakarohaina te \left(-5b\right)^{2}.

$$-19b^{2}+4ab+\left(-5\right)^{2}b^{2}$$

Tātaihia te -5 mā te pū o 2, kia riro ko 25.

$$-19b^{2}+4ab+25b^{2}$$

Pahekotia te -19b^{2} me 25b^{2}, ka 6b^{2}.

$$6b^{2}+4ab$$