Whakaoti i te 3(2x+5)^2-4(2x+5)(2x-5)+10(2x-5)^2=

$$3 ( 2 x + 5 ) ^ { 2 } - 4 ( 2 x + 5 ) ( 2 x - 5 ) + 10 ( 2 x - 5 ) ^ { 2 } =$$

Aromātai

$$36x^{2}-140x+425$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+5\right)^{2}.

$$3\left(4x^{2}+20x+25\right)-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 4x^{2}+20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(4x^{2}-20x+25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 10 ki te 4x^{2}-20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+40x^{2}-200x+250$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te 2x+5.

$$12x^{2}+60x+75+\left(-8x-20\right)\left(2x-5\right)+40x^{2}-200x+250$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -8x-20 ki te 2x-5 ka whakakotahi i ngā kupu rite.

$$12x^{2}+60x+75-16x^{2}+100+40x^{2}-200x+250$$

Pahekotia te 12x^{2} me -16x^{2}, ka -4x^{2}.

$$-4x^{2}+60x+75+100+40x^{2}-200x+250$$

Tāpirihia te 75 ki te 100, ka 175.

$$-4x^{2}+60x+175+40x^{2}-200x+250$$

Pahekotia te -4x^{2} me 40x^{2}, ka 36x^{2}.

$$36x^{2}+60x+175-200x+250$$

Pahekotia te 60x me -200x, ka -140x.

$$36x^{2}-140x+175+250$$

Tāpirihia te 175 ki te 250, ka 425.

$$36x^{2}-140x+425$$

Whakaroha

$$36x^{2}-140x+425$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+5\right)^{2}.

$$3\left(4x^{2}+20x+25\right)-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 4x^{2}+20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(2x-5\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+10\left(4x^{2}-20x+25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 10 ki te 4x^{2}-20x+25.

$$12x^{2}+60x+75-4\left(2x+5\right)\left(2x-5\right)+40x^{2}-200x+250$$

Whakamahia te āhuatanga tohatoha hei whakarea te -4 ki te 2x+5.

$$12x^{2}+60x+75+\left(-8x-20\right)\left(2x-5\right)+40x^{2}-200x+250$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -8x-20 ki te 2x-5 ka whakakotahi i ngā kupu rite.

$$12x^{2}+60x+75-16x^{2}+100+40x^{2}-200x+250$$

Pahekotia te 12x^{2} me -16x^{2}, ka -4x^{2}.

$$-4x^{2}+60x+75+100+40x^{2}-200x+250$$

Tāpirihia te 75 ki te 100, ka 175.

$$-4x^{2}+60x+175+40x^{2}-200x+250$$

Pahekotia te -4x^{2} me 40x^{2}, ka 36x^{2}.

$$36x^{2}+60x+175-200x+250$$

Pahekotia te 60x me -200x, ka -140x.

$$36x^{2}-140x+175+250$$

Tāpirihia te 175 ki te 250, ka 425.

$$36x^{2}-140x+425$$