Issolvi 3(2x+5)^2-4(2x+5)(2x-5)+10(2x-5)^2=

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

Evalwa

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2x+5\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 3 b'4x^{2}+20x+25.

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2x-5\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 10 b'4x^{2}-20x+25.

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

Uża l-propjetà distributtiva biex timmultiplika -4 b'2x+5.

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

Uża l-propjetà distributtiva biex timmultiplika -8x-20 b'2x-5 u kkombina termini simili.

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

Ikkombina 12x^{2} u -16x^{2} biex tikseb -4x^{2}.

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

Żid 75 u 100 biex tikseb 175.

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

Ikkombina -4x^{2} u 40x^{2} biex tikseb 36x^{2}.

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

Ikkombina 60x u -200x biex tikseb -140x.

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

Żid 175 u 250 biex tikseb 425.

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

Espandi

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

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(2x+5\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 3 b'4x^{2}+20x+25.

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

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2x-5\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 10 b'4x^{2}-20x+25.

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

Uża l-propjetà distributtiva biex timmultiplika -4 b'2x+5.

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

Uża l-propjetà distributtiva biex timmultiplika -8x-20 b'2x-5 u kkombina termini simili.

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

Ikkombina 12x^{2} u -16x^{2} biex tikseb -4x^{2}.

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

Żid 75 u 100 biex tikseb 175.

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

Ikkombina -4x^{2} u 40x^{2} biex tikseb 36x^{2}.

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

Ikkombina 60x u -200x biex tikseb -140x.

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

Żid 175 u 250 biex tikseb 425.

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